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Best length of individual cycle:

     5           1           1          -1              2   3.598813   0.5557389
    17           1           3          -2              6   11.68164   0.5136266
    41           1           5          -4             10   23.77846   0.4205486
    73           1           7          -6             18   36.6577    0.4910291
   193           1          13          -6             30   73.11163   0.4103314
   241           1          15          -4             38   85.14695   0.4462873
   337           1          17         -12             42   106.8425   0.3931019
   409           1          19         -12             54   121.6199   0.4440064
   601           1          23         -18             66   156.8635   0.420748
   769           1          27         -10             70   184.274    0.3798691
  1033           1          31         -18             78   223.061    0.3496802
  1201           1          33         -28            106   245.7386   0.4313526
  1609           1          39         -22            118   296.1642   0.3984276
  1801           1          41         -30            130   318.1208   0.4086498
  2161           1          45         -34            146   356.939    0.4090335
  2521           1          49         -30            170   393.2619   0.4322819
  3361           1          57         -28            178   470.7496   0.3781203
  3529           1          59         -12            198   485.2689   0.4080212
  4201           1          63         -58            210   540.7576   0.3883441
  4561           1          67         -18            214   569.0039   0.3760958
  5209           1          71         -42            238   617.6703   0.3853188
  5569           1          73         -60            258   643.6448   0.4008422
  6841           1          81         -70            290   730.3893   0.3970485
  7561           1          85         -84            306   776.5653   0.3940428
  8089           1          89         -42            330   809.2934   0.4077631
  9241           1          95         -54            346   877.8031   0.3941658
 12049           1         109         -42            378   1031.46    0.3664707
 12289           1         109        -102            390   1043.869   0.3736102
 12601           1         111         -70            394   1059.851   0.3717503
 13729           1         117         -10            426   1116.317   0.3816119
 15649           1         125          -6            454   1208.197   0.3757665
 16921           1         129         -70            474   1266.507   0.3742578
 18481           1         135         -64            502   1335.59    0.3758639
 19009           1         137         -60            522   1358.418   0.3842705
 20161           1         141         -70            530   1407.329   0.3765999
 21121           1         145         -24            542   1447.206   0.3745147
 21961           1         147         -88            566   1481.483   0.3820495
 24049           1         155          -6            578   1564.397   0.3694714
 26041           1         161         -30            590   1640.741   0.3595937
 26161           1         161         -60            602   1645.26    0.3658996
 28081           1         167         -48            622   1716.434   0.3623793
 28729           1         169         -42            630   1739.992   0.3620706
 31249           1         175        -156            674   1829.564   0.3683938
 33049           1         181         -72            702   1891.701   0.3710947
 33289           1         181        -132            714   1899.877   0.3758138
 38329           1         195         -76            722   2066.233   0.3494282
 40609           1         201         -52            750   2138.444   0.3507222
 43201           1         207         -88            766   2218.496   0.345279
 43801           1         209         -30            794   2236.735   0.3549817
 47041           1         215        -204            842   2333.464   0.3608369
 47881           1         217        -198            862   2358.079   0.3655518
 48049           1         219         -22            878   2362.98    0.3715648
 49009           1         221         -42            886   2390.848   0.3705798
 51769           1         227         -60            914   2469.714   0.3700834
 53881           1         231        -130            966   2528.87    0.3819888
 59929           1         243        -220            974   2693.068   0.3616693
 61681           1         247        -168           1002   2739.307   0.365786
 65521           1         255        -124           1006   2838.747   0.3543817
 66361           1         257         -78           1022   2860.168   0.3573217
 67369           1         259         -72           1042   2885.721   0.3610882
 69001           1         261        -220           1074   2926.753   0.3669596
 70849           1         265        -156           1086   2972.721   0.3653219
 80809           1         283        -180           1142   3212.198   0.3555198
 87481           1         295        -114           1242   3365.64    0.3690234
101641           1         317        -288           1246   3675.646   0.338988
101929           1         319         -42           1270   3681.754   0.3449443
102001           1         319         -60           1298   3683.279   0.3524034

Best length of individual cycle: let d be the discriminant, a,b,c the coefficients of the form considered, L the length of the cycle, cohn = sqrt(d) log(d), and ratio = L/cohn

     d           a           b           c              L    cohn       ratio
     5           1           1          -1              2   3.598813   0.5557389
    17           1           3          -2              6   11.68164   0.5136266
    41           1           5          -4             10   23.77846   0.4205486
    73           1           7          -6             18   36.6577    0.4910291
   193           1          13          -6             30   73.11163   0.4103314
   241           1          15          -4             38   85.14695   0.4462873
   337           1          17         -12             42   106.8425   0.3931019
   409           1          19         -12             54   121.6199   0.4440064
   601           1          23         -18             66   156.8635   0.420748
   769           1          27         -10             70   184.274    0.3798691
  1033           1          31         -18             78   223.061    0.3496802
  1201           1          33         -28            106   245.7386   0.4313526
  1609           1          39         -22            118   296.1642   0.3984276
  1801           1          41         -30            130   318.1208   0.4086498
  2161           1          45         -34            146   356.939    0.4090335
  2521           1          49         -30            170   393.2619   0.4322819
  3361           1          57         -28            178   470.7496   0.3781203
  3529           1          59         -12            198   485.2689   0.4080212
  4201           1          63         -58            210   540.7576   0.3883441
  4561           1          67         -18            214   569.0039   0.3760958
  5209           1          71         -42            238   617.6703   0.3853188
  5569           1          73         -60            258   643.6448   0.4008422
  6841           1          81         -70            290   730.3893   0.3970485
  7561           1          85         -84            306   776.5653   0.3940428
  8089           1          89         -42            330   809.2934   0.4077631
  9241           1          95         -54            346   877.8031   0.3941658
 12049           1         109         -42            378   1031.46    0.3664707
 12289           1         109        -102            390   1043.869   0.3736102
 12601           1         111         -70            394   1059.851   0.3717503
 13729           1         117         -10            426   1116.317   0.3816119
 15649           1         125          -6            454   1208.197   0.3757665
 16921           1         129         -70            474   1266.507   0.3742578
 18481           1         135         -64            502   1335.59    0.3758639
 19009           1         137         -60            522   1358.418   0.3842705
 20161           1         141         -70            530   1407.329   0.3765999
 21121           1         145         -24            542   1447.206   0.3745147
 21961           1         147         -88            566   1481.483   0.3820495
 24049           1         155          -6            578   1564.397   0.3694714
 26041           1         161         -30            590   1640.741   0.3595937
 26161           1         161         -60            602   1645.26    0.3658996
 28081           1         167         -48            622   1716.434   0.3623793
 28729           1         169         -42            630   1739.992   0.3620706
 31249           1         175        -156            674   1829.564   0.3683938
 33049           1         181         -72            702   1891.701   0.3710947
 33289           1         181        -132            714   1899.877   0.3758138
 38329           1         195         -76            722   2066.233   0.3494282
 40609           1         201         -52            750   2138.444   0.3507222
 43201           1         207         -88            766   2218.496   0.345279
 43801           1         209         -30            794   2236.735   0.3549817
 47041           1         215        -204            842   2333.464   0.3608369
 47881           1         217        -198            862   2358.079   0.3655518
 48049           1         219         -22            878   2362.98    0.3715648
 49009           1         221         -42            886   2390.848   0.3705798
 51769           1         227         -60            914   2469.714   0.3700834
 53881           1         231        -130            966   2528.87    0.3819888
 59929           1         243        -220            974   2693.068   0.3616693
 61681           1         247        -168           1002   2739.307   0.365786
 65521           1         255        -124           1006   2838.747   0.3543817
 66361           1         257         -78           1022   2860.168   0.3573217
 67369           1         259         -72           1042   2885.721   0.3610882
 69001           1         261        -220           1074   2926.753   0.3669596
 70849           1         265        -156           1086   2972.721   0.3653219
 80809           1         283        -180           1142   3212.198   0.3555198
 87481           1         295        -114           1242   3365.64    0.3690234
101641           1         317        -288           1246   3675.646   0.338988
101929           1         319         -42           1270   3681.754   0.3449443
102001           1         319         -60           1298   3683.279   0.3524034
     d           a           b           c              L    cohn       ratio

jagy@phobeusjunior:~$ 
      d    red  red/(sqrt(d) log(d))
      5      2   0.555739    5 = 5
     12      4   0.464686    12 = 2^2 * 3
     17      6   0.513627    17 = 17
     28      8   0.453711    28 = 2^2 * 7
     41     10   0.420549    41 = 41
     57     12   0.393129    57 = 3 * 19
     73     18   0.491029    73 = 73
    105     20   0.419385    105 = 3 * 5 * 7
    145     28   0.467229    145 = 5 * 29
    193     30   0.410331    193 = 193
    217     32   0.403781    217 = 7 * 31
    241     38   0.446287    241 = 241
    265     40   0.440376    265 = 5 * 53
    337     42   0.393102    337 = 337
    385     44   0.376677    385 = 5 * 7 * 11
    409     54   0.444006    409 = 409
    481     56   0.413445    481 = 13 * 37
    505     60   0.42894     505 = 5 * 101
    601     66   0.420748    601 = 601
    649     68   0.412209    649 = 11 * 59
    721     72   0.407471    721 = 7 * 103
    865     80   0.402217    865 = 5 * 173
    889     84   0.414909    889 = 7 * 127
   1009     90   0.409635    1009 = 1009
   1081     92   0.400561    1081 = 23 * 47
   1129    102   0.431871    1129 = 1129
   1201    106   0.431353    1201 = 1201
   1489    114   0.404377    1489 = 1489
   1609    118   0.398428    1609 = 1609
   1801    130   0.40865     1801 = 1801
   1969    140   0.415943    1969 = 11 * 179
   2161    146   0.409034    2161 = 2161
   2521    170   0.432282    2521 = 2521
   3241    180   0.391135    3241 = 7 * 463
   3529    198   0.408021    3529 = 3529
   3649    208   0.419803    3649 = 41 * 89
   4201    210   0.388344    4201 = 4201
   4321    216   0.392529    4321 = 29 * 149
   4369    220   0.397072    4369 = 17 * 257
   4729    230   0.395273    4729 = 4729
   5209    238   0.385319    5209 = 5209
   5401    240   0.379981    5401 = 11 * 491
   5569    258   0.400842    5569 = 5569
   6049    264   0.389817    6049 = 23 * 263
   6169    272   0.396809    6169 = 31 * 199
   6769    276   0.380341    6769 = 7 * 967
   6841    290   0.397049    6841 = 6841
   7561    306   0.394043    7561 = 7561
   8089    330   0.407763    8089 = 8089
   9241    346   0.394166    9241 = 9241
   9529    352   0.393572    9529 = 13 * 733
  10921    380   0.391059    10921 = 67 * 163
  12289    390   0.37361     12289 = 12289
  12601    394   0.37175     12601 = 12601
  12961    404   0.374736    12961 = 13 * 997
  13729    426   0.381612    13729 = 13729
  14281    434   0.37962     14281 = 14281
  14569    448   0.387165    14569 = 17 * 857
  15409    472   0.394326    15409 = 19 * 811
  15961    480   0.392582    15961 = 11 * 1451
  17329    492   0.382933    17329 = 13 * 31 * 43
  18001    516   0.392515    18001 = 47 * 383
  19009    522   0.38427     19009 = 19009
  20161    530   0.3766      20161 = 20161
  20689    532   0.372195    20689 = 17 * 1217
  21121    542   0.374515    21121 = 21121
  21961    566   0.38205     21961 = 21961
  23689    574   0.370245    23689 = 23689
  23809    576   0.370412    23809 = 29 * 821
  23881    584   0.374878    23881 = 11 * 13 * 167
  25249    596   0.370028    25249 = 7 * 3607
  26161    602   0.3659      26161 = 26161
  27049    616   0.367007    27049 = 11 * 2459
  28081    622   0.362379    28081 = 28081
  28681    660   0.379691    28681 = 23 * 29 * 43
  31201    680   0.372014    31201 = 41 * 761
  33049    702   0.371095    33049 = 33049
  33289    714   0.375814    33289 = 33289
  37129    752   0.3709      37129 = 107 * 347
  37801    756   0.368915    37801 = 103 * 367
  40441    768   0.360025    40441 = 37 * 1093
  40681    776   0.362499    40681 = 17 * 2393
  43801    794   0.354982    43801 = 43801
  43849    808   0.361006    43849 = 13 * 3373
  44209    812   0.361037    44209 = 11 * 4019
  44641    826   0.365148    44641 = 44641
  45049    848   0.372856    45049 = 19 * 2371
  46561    852   0.36735     46561 = 101 * 461
  47881    862   0.365552    47881 = 47881
  48049    878   0.371565    48049 = 48049
  49009    886   0.37058     49009 = 49009
  50521    912   0.374649    50521 = 19 * 2659
  51769    914   0.370083    51769 = 51769
  53881    966   0.381989    53881 = 53881
  58969    984   0.368886    58969 = 109 * 541
  61681   1002   0.365786    61681 = 61681
  63361   1022   0.367213    63361 = 63361
  65209   1040   0.367392    65209 = 61 * 1069
  65641   1052   0.370186    65641 = 41 * 1601
  69001   1074   0.36696     69001 = 69001
  70849   1086   0.365322    70849 = 70849
  74281   1100   0.359858    74281 = 59 * 1259
  74881   1128   0.367273    74881 = 103 * 727
  77401   1144   0.365291    77401 = 17 * 29 * 157
  81481   1180   0.365564    81481 = 17 * 4793
  84529   1200   0.363814    84529 = 137 * 617
  85801   1212   0.364239    85801 = 239 * 359
  86641   1252   0.374111    86641 = 23 * 3767
  92569   1286   0.369611    92569 = 92569
  95209   1296   0.366384    95209 = 19 * 5011
 100321   1320   0.361886    100321 = 13 * 7717
      d    red  red/(sqrt(d) log(d))
jagy@phobeusjunior:~$

file named many_reduced_binary.txt 
        d       red  red/(sqrt(d) log(d)) 
        5         2       0.555739              5 = 5
       12         4       0.464686             12 = 2^2 * 3
       17         6       0.513627             17 = 17
       28         8       0.453711             28 = 2^2 * 7
       41        10       0.420549             41 = 41
       57        12       0.393129             57 = 3 * 19
       73        18       0.491029             73 = 73
      105        20       0.419385            105 = 3 * 5 * 7
      145        28       0.467229            145 = 5 * 29
      193        30       0.410331            193 = 193
      217        32       0.403781            217 = 7 * 31
      241        38       0.446287            241 = 241
      265        40       0.440376            265 = 5 * 53
      337        42       0.393102            337 = 337
      385        44       0.376677            385 = 5 * 7 * 11
      409        54       0.444006            409 = 409
      481        56       0.413445            481 = 13 * 37
      505        60        0.42894            505 = 5 * 101
      601        66       0.420748            601 = 601
      649        68       0.412209            649 = 11 * 59
      721        72       0.407471            721 = 7 * 103
      865        80       0.402217            865 = 5 * 173
      889        84       0.414909            889 = 7 * 127
     1009        90       0.409635           1009 = 1009
     1081        92       0.400561           1081 = 23 * 47
     1129       102       0.431871           1129 = 1129
     1201       106       0.431353           1201 = 1201
     1489       114       0.404377           1489 = 1489
     1609       118       0.398428           1609 = 1609
     1801       130        0.40865           1801 = 1801
     1969       140       0.415943           1969 = 11 * 179
     2161       146       0.409034           2161 = 2161
     2521       170       0.432282           2521 = 2521
     3241       180       0.391135           3241 = 7 * 463
     3529       198       0.408021           3529 = 3529
     3649       208       0.419803           3649 = 41 * 89
     4201       210       0.388344           4201 = 4201
     4321       216       0.392529           4321 = 29 * 149
     4369       220       0.397072           4369 = 17 * 257
     4729       230       0.395273           4729 = 4729
     5209       238       0.385319           5209 = 5209
     5401       240       0.379981           5401 = 11 * 491
     5569       258       0.400842           5569 = 5569
     6049       264       0.389817           6049 = 23 * 263
     6169       272       0.396809           6169 = 31 * 199
     6769       276       0.380341           6769 = 7 * 967
     6841       290       0.397049           6841 = 6841
     7561       306       0.394043           7561 = 7561
     8089       330       0.407763           8089 = 8089
     9241       346       0.394166           9241 = 9241
     9529       352       0.393572           9529 = 13 * 733
    10921       380       0.391059          10921 = 67 * 163
    12289       390        0.37361          12289 = 12289
    12601       394        0.37175          12601 = 12601
    12961       404       0.374736          12961 = 13 * 997
    13729       426       0.381612          13729 = 13729
    14281       434        0.37962          14281 = 14281
    14569       448       0.387165          14569 = 17 * 857
    15409       472       0.394326          15409 = 19 * 811
    15961       480       0.392582          15961 = 11 * 1451
    17329       492       0.382933          17329 = 13 * 31 * 43
    18001       516       0.392515          18001 = 47 * 383
    19009       522        0.38427          19009 = 19009
    20161       530         0.3766          20161 = 20161
    20689       532       0.372195          20689 = 17 * 1217
    21121       542       0.374515          21121 = 21121
    21961       566        0.38205          21961 = 21961
    23689       574       0.370245          23689 = 23689
    23809       576       0.370412          23809 = 29 * 821
    23881       584       0.374878          23881 = 11 * 13 * 167
    25249       596       0.370028          25249 = 7 * 3607
    26161       602         0.3659          26161 = 26161
    27049       616       0.367007          27049 = 11 * 2459
    28081       622       0.362379          28081 = 28081
    28681       660       0.379691          28681 = 23 * 29 * 43
    31201       680       0.372014          31201 = 41 * 761
    33049       702       0.371095          33049 = 33049
    33289       714       0.375814          33289 = 33289
    37129       752         0.3709          37129 = 107 * 347
    37801       756       0.368915          37801 = 103 * 367
    40441       768       0.360025          40441 = 37 * 1093
    40681       776       0.362499          40681 = 17 * 2393
    43801       794       0.354982          43801 = 43801
    43849       808       0.361006          43849 = 13 * 3373
    44209       812       0.361037          44209 = 11 * 4019
    44641       826       0.365148          44641 = 44641
    45049       848       0.372856          45049 = 19 * 2371
    46561       852        0.36735          46561 = 101 * 461
    47881       862       0.365552          47881 = 47881
    48049       878       0.371565          48049 = 48049
    49009       886        0.37058          49009 = 49009
    50521       912       0.374649          50521 = 19 * 2659
    51769       914       0.370083          51769 = 51769
    53881       966       0.381989          53881 = 53881
    58969       984       0.368886          58969 = 109 * 541
    61681      1002       0.365786          61681 = 61681
    63361      1022       0.367213          63361 = 63361
    65209      1040       0.367392          65209 = 61 * 1069
    65641      1052       0.370186          65641 = 41 * 1601
    69001      1074        0.36696          69001 = 69001
    70849      1086       0.365322          70849 = 70849
    74281      1100       0.359858          74281 = 59 * 1259
    74881      1128       0.367273          74881 = 103 * 727
    77401      1144       0.365291          77401 = 17 * 29 * 157
    81481      1180       0.365564          81481 = 17 * 4793
    84529      1200       0.363814          84529 = 137 * 617
    85801      1212       0.364239          85801 = 239 * 359
    86641      1252       0.374111          86641 = 23 * 3767
    92569      1286       0.369611          92569 = 92569
    95209      1296       0.366384          95209 = 19 * 5011
   100321      1320       0.361886         100321 = 13 * 7717
   105169      1328       0.354137         105169 = 251 * 419
   105361      1330       0.354291         105361 = 105361
   109729      1360       0.353756         109729 = 197 * 557
   111721      1378       0.354679         111721 = 111721
   114409      1396       0.354341         114409 = 191 * 599
   117049      1496       0.374683         117049 = 67 * 1747
   127009      1516       0.361968         127009 = 107 * 1187
   130729      1558       0.365766         130729 = 130729
   138121      1584       0.360101         138121 = 37 * 3733
   144169      1610        0.35696         144169 = 144169
   153169      1672       0.357826         153169 = 89 * 1721
   155401      1676       0.355666         155401 = 19 * 8179
   157249      1680       0.354064         157249 = 67 * 2347
   157921      1736       0.364956         157921 = 79 * 1999
   173209      1814       0.361346         173209 = 173209
   180049      1852       0.360682         180049 = 401 * 449
   185641      1902       0.363879         185641 = 185641
   197521      1910       0.352448         197521 = 197521
   204649      1916       0.346336         204649 = 19 * 10771
   204961      1948       0.351809         204961 = 97 * 2113
   210961      1978       0.351281         210961 = 210961
   220081      1992       0.345168         220081 = 29 * 7589
   223609      2104       0.361221         223609 = 311 * 719
   242449      2114       0.346277         242449 = 242449
   251329      2144       0.343934         251329 = 13 * 19333
   259009      2170       0.342077         259009 = 259009
   261361      2200       0.344992         261361 = 31 * 8431
   266809      2216       0.343367         266809 = 367 * 727
   268129      2272       0.351037         268129 = 73 * 3673
   279889      2316       0.349039         279889 = 19 * 14731
   287401      2396       0.355594         287401 = 31 * 73 * 127
   295201      2398       0.350411         295201 = 295201
   306289      2412       0.345008         306289 = 17 * 43 * 419
   314161      2446       0.344768         314161 = 314161
   315121      2452       0.345004         315121 = 181 * 1741
   316369      2476       0.347584         316369 = 19 * 16651
   320401      2534       0.353128         320401 = 320401
   328441      2600       0.357165         328441 = 53 * 6197
   349801      2602       0.344645         349801 = 349801
   357361      2656       0.347474         357361 = 191 * 1871
   360721      2664        0.34664         360721 = 137 * 2633
   367249      2692       0.346671         367249 = 181 * 2029
   373129      2700       0.344523         373129 = 23 * 16223
   383881      2716       0.340922         383881 = 103 * 3727
   389041      2730       0.340046         389041 = 389041
   393121      2782       0.344441         393121 = 393121
   394969      2866       0.353881         394969 = 394969
   415801      2878       0.344971         415801 = 415801
   416329      2936       0.351665         416329 = 263 * 1583
   425569      2952        0.34913         425569 = 23 * 18503
   457081      2996       0.340027         457081 = 83 * 5507
   463849      2998       0.337382         463849 = 463849
   465481      3008       0.337823         465481 = 19 * 24499
   469249      3032       0.338939         469249 = 11 * 29 * 1471
   469561      3038       0.339479         469561 = 469561
   483289      3154       0.346635         483289 = 483289
   503281      3212       0.344859         503281 = 463 * 1087
   511681      3244       0.344989         511681 = 23 * 22247
   515761      3330       0.352519         515761 = 515761
   528889      3336       0.348078         528889 = 167 * 3167
   540409      3348       0.345023         540409 = 439 * 1231
   552841      3386         0.3444         552841 = 552841
   563161      3432       0.345382         563161 = 233 * 2417
   579049      3448       0.341481         579049 = 31 * 18679
   600601      3542       0.343493         600601 = 600601
   601129      3560       0.345064         601129 = 509 * 1181
   605641      3570       0.344549         605641 = 605641
   628489      3668       0.346549         628489 = 41 * 15329
   663961      3706       0.339262         663961 = 663961
   677161      3728       0.337438         677161 = 17 * 61 * 653
   685441      3812       0.342641         685441 = 31 * 22111
   691681      3846       0.343902         691681 = 691681
   702529      3866       0.342615         702529 = 702529
   722929      3920       0.341737         722929 = 79 * 9151
   723529      3950       0.344188         723529 = 723529
   766921      4004       0.337423         766921 = 17 * 197 * 229
   772489      4024       0.337704         772489 = 31 * 24919
   786241      4134       0.343441         786241 = 786241
   799681      4136       0.340283         799681 = 37 * 21613
   819289      4174       0.338671         819289 = 819289
   825841      4256       0.343751         825841 = 379 * 2179
   878641      4398       0.342822         878641 = 878641
   914281      4416       0.336472         914281 = 337 * 2713
   924169      4444       0.336525         924169 = 881 * 1049
   928489      4528       0.341971         928489 = 17 * 54617
   969049      4590       0.338269         969049 = 969049
   979969      4698       0.344014         979969 = 979969
  1007161      4706       0.339243        1007161 = 1007161
  1057081      4792       0.336012        1057081 = 157 * 6733
  1083289      4966       0.343368        1083289 = 1083289
  1162561      4988        0.33124        1162561 = 103 * 11287
  1171921      5070       0.335145        1171921 = 1171921
  1195489      5118        0.33449        1195489 = 1195489
  1201561      5300       0.345384        1201561 = 541 * 2221
  1264561      5322       0.336838        1264561 = 1264561
  1267249      5424       0.342878        1267249 = 31 * 40879
  1354369      5468       0.332783        1354369 = 73 * 18553
  1354609      5480       0.333479        1354609 = 71 * 19079
  1368481      5532       0.334692        1368481 = 29 * 47189
  1379569      5576       0.335803        1379569 = 43 * 32083
  1391329      5624       0.337057        1391329 = 83 * 16763
  1433041      5826       0.343328        1433041 = 1433041
  1466089      5856       0.340636        1466089 = 23 * 63743
  1538161      5864       0.331892        1538161 = 1063 * 1447
  1552849      5900       0.332125        1552849 = 229 * 6781
  1577689      5910       0.329692        1577689 = 1577689
  1609609      5920         0.3265        1609609 = 23 * 47 * 1489
  1627921      6120       0.335362        1627921 = 571 * 2851
  1642369      6132       0.334331        1642369 = 433 * 3793
  1672609      6158       0.332276        1672609 = 1672609
  1699681      6210       0.332031        1699681 = 1699681
  1701001      6232        0.33306        1701001 = 31 * 37 * 1483
  1719481      6240       0.331441        1719481 = 19 * 90499
  1720489      6304       0.334729        1720489 = 97 * 17737
  1739929      6312       0.333015        1739929 = 83 * 20963
  1785169      6444       0.335045        1785169 = 149 * 11981
  1848289      6534       0.333069        1848289 = 1848289
  1851529      6604       0.336302        1851529 = 167 * 11087
  1906129      6768       0.338999        1906129 = 37 * 51517
  2031649      6964       0.336386        2031649 = 53 * 38333
  2144041      7062       0.330832        2144041 = 2144041
  2159161      7128       0.332592        2159161 = 1117 * 1933
  2213929      7156       0.329177        2213929 = 433 * 5113
  2222089      7226       0.331703        2222089 = 2222089
  2235601      7236       0.331019        2235601 = 569 * 3929
  2293729      7402       0.333709        2293729 = 2293729
  2356201      7408       0.328919        2356201 = 479 * 4919
  2413321      7604       0.333058        2413321 = 23 * 317 * 331
  2490049      7620       0.327878        2490049 = 23 * 108263
  2519449      7636       0.326384        2519449 = 73 * 34513
  2545321      7772       0.330275        2545321 = 41 * 62081
  2602681      7886       0.330907        2602681 = 2602681
  2636209      7892       0.328761        2636209 = 31 * 277 * 307
  2675401      7952       0.328497        2675401 = 281 * 9521
  2770681      8060       0.326412        2770681 = 53 * 61 * 857
  2784961      8234       0.332487        2784961 = 2784961
  2922529      8254       0.324302        2922529 = 2922529
  2938849      8348       0.326961        2938849 = 59 * 49811
  2959441      8468        0.33035        2959441 = 383 * 7727
  2985889      8548       0.331793        2985889 = 31 * 61 * 1579
  3100969      8596       0.326578        3100969 = 1319 * 2351
  3147769      8604       0.324118        3147769 = 1123 * 2803
  3197041      8664       0.323518        3197041 = 397 * 8053
  3199681      8708       0.325009        3199681 = 41 * 78041
  3206641      8788       0.327591        3206641 = 643 * 4987
  3267289      8810       0.324942        3267289 = 3267289
  3335929      9140       0.333166        3335929 = 101 * 33029
  3395401      9220       0.332734        3395401 = 709 * 4789
  3528001      9242       0.326369        3528001 = 3528001
  3581449      9356       0.327593        3581449 = 89 * 40241
  3674449      9412       0.324805        3674449 = 227 * 16187
  3712921      9628       0.330306        3712921 = 43 * 79 * 1093
  3818929      9818       0.331499        3818929 = 3818929
  3864169      9860       0.330706        3864169 = 37 * 181 * 577
  4064449      9904       0.322818        4064449 = 883 * 4603
  4217929      9910       0.316312        4217929 = 4217929
  4269841     10050       0.318569        4269841 = 4269841
  4270561     10092        0.31987        4270561 = 47 * 90863
  4275049     10150       0.321518        4275049 = 4275049
  4280329     10378        0.32851        4280329 = 4280329
  4499881     10420       0.320642        4499881 = 23 * 179 * 1093
  4586761     10660       0.324501        4586761 = 563 * 8147
  4701841     10770        0.32329        4701841 = 4701841
  4708729     10830       0.324822        4708729 = 4708729
  4724281     10932       0.327271        4724281 = 43 * 181 * 607
  4861081     11056       0.325688        4861081 = 859 * 5659
  4962049     11062       0.322102        4962049 = 4962049
  5013649     11082       0.320805        5013649 = 5013649
  5048761     11220       0.323522        5048761 = 37 * 136453
  5098129     11354       0.325591        5098129 = 5098129
  5343529     11410       0.318626        5343529 = 5343529
  5368609     11438       0.318564        5368609 = 5368609
  5390449     11566       0.321392        5390449 = 5390449
  5505361     11602       0.318577        5505361 = 5505361
  5542681     11684       0.319607        5542681 = 293 * 18917
  5587201     11744       0.319801        5587201 = 73 * 76537
  5634841     11984       0.324777        5634841 = 37 * 152293
  5730169     12104       0.324938        5730169 = 233 * 24593
  5815681     12308       0.327664        5815681 = 71 * 101 * 811
  6016921     12418       0.324309        6016921 = 6016921
  6080881     12430       0.322692        6080881 = 6080881
  6104641     12586       0.326024        6104641 = 6104641
  6195289     12648       0.324918        6195289 = 67 * 92467
  6406009     12912       0.325503        6406009 = 199 * 32191
  6589969     13026       0.323177        6589969 = 6589969
  6763849     13046       0.318957        6763849 = 6763849
  6783529     13194       0.322047        6783529 = 6783529
  6868801     13434       0.325605        6868801 = 6868801
  6969169     13504       0.324637        6969169 = 967 * 7207
  7209409     13856       0.326799        7209409 = 127 * 56767
  7478689     14180       0.327604        7478689 = 43 * 173923
  7623529     14206       0.324679        7623529 = 7623529
  7880161     14332       0.321509        7880161 = 47 * 167663
  7926361     14420        0.32242        7926361 = 359 * 22079
  8092681     14484       0.320087        8092681 = 79 * 89 * 1151
  8254801     14666       0.320511        8254801 = 8254801
  8281729     14724        0.32119        8281729 = 47 * 176207
  8465209     15118       0.325743        8465209 = 8465209
  8895769     15350       0.321638        8895769 = 8895769
  9033649     15706       0.326263        9033649 = 9033649
  9257329     15854       0.324838        9257329 = 9257329
  9850801     15906       0.314714        9850801 = 9850801
  9853561     15992       0.316366        9853561 = 173 * 56957
 10018849     16024       0.314049       10018849 = 47 * 59 * 3613
 10058161     16340       0.319538       10058161 = 41 * 245321
 10319761     16586       0.319702       10319761 = 10319761

=======================================================

Wikipedia lists two articles on maximum length for the continued fraction of $\sqrt n,$ Hickerson 1973 and Cohn 1977. There is a mess in the references, Cohn is not visible, just the link.

Hickerson and Cohn say that the period length for $\sqrt d$ is below $\sqrt d \log d.$ My own computations say this for both cycles of arbitrary redcued forms and total count of fomrs, where the latter has slightly larger implied constant (maybe over Cohn's $\frac{7}{2 \pi^2}.$ So the questions are, is $C_j \sqrt d \log d$ a provable upper bound for my two related problems?

Wikipedia lists two articles on maximum length for the continued fraction of $\sqrt n,$ Hickerson 1973 and Cohn 1977. There is a mess in the references, Cohn is not visible, just the link.

Hickerson and Cohn say that the period length for $\sqrt d$ is below $\sqrt d \log d.$ My own computations say this for both cycles of arbitrary reduced forms and total count of forms, where the latter has slightly larger implied constant (maybe over Cohn's $\frac{7}{2 \pi^2}.$ So the questions are, is $C_j \sqrt d \log d$ a provable upper bound for my two related problems?