Hi, David. This is roughly Robin's comment, just with longer discussions, and, I am afraid, links to my own answers. That's life. I think you would probably enjoy J.H. Conway, "The Sensual Quadratic Form," especially PSL_2(Z) on pages 27-33. I always like "The Markoff and Lagrange Spectra" by Thomas W. Cusick and Mary E. Flahive and "Binary Quadratic Forms" by Duncan A. Buell. On particular issues I think you are raising, answers by me and by Dror in: Reasons for switching from simple continued fractions for $\sqrt D$ to reduced forms: http://mathoverflow.net/questions/22811/ Numbers (here primes) occurring as "diagonal" coefficients: http://mathoverflow.net/questions/29850/ Other: http://mathoverflow.net/questions/22552/ In my language, I think you are asking mostly about small numbers occurring as diagonal coefficients, just not necessarily prime. For me, such numbers need also to be *primitively* represented by the forms in the cycle (for you I guess it is by $ x^2 - D y^2 ,$ using $a_0 = \lfloor \sqrt D \rfloor$ your quadratic form is equivalent to the reduced form $\langle 1,\; 2 a_0, \; a_0^2 - D \rangle.$ ) phoebus:~/Cplusplus> ./Pell Input n for Pell 67 0 form 1 16 -3 delta -5 1 form -3 14 6 delta 2 2 form 6 10 -7 delta -1 3 form -7 4 9 delta 1 4 form 9 14 -2 delta -7 5 form -2 14 9 delta 1 6 form 9 4 -7 delta -1 7 form -7 10 6 delta 2 8 form 6 14 -3 delta -5 9 form -3 16 1 delta 16 10 form 1 16 -3 disc 268 Automorph, written on right of Gram matrix: -1106 -17901 -5967 -96578 Pell automorph -48842 -399789 -5967 -48842 Pell unit -48842^2 - 67 * -5967^2 = 1 ========================================= Anyway, let me know if you want to see any more worked examples.