We are searching for the rank 8 elliptic curves with the torsion subgroup Z/6 using newly discovered families similar to Kihara's (Kihara's family is described in https://arxiv.org/pdf/1503.03667.pdf).

Today we came across a curve

$[0,8169768624655967629114128598,0,-451787550647310420612086468536366715869054405951830599,0]$

Both Magma Calculator (http://magma.maths.usyd.edu.au/calc/) and mwrank with $-b12$ return 6 generators for this curve. Magma V2.20-10 (STUDENT) runs out of memory running the following code:

```
SetClassGroupBounds("GRH");
E := EllipticCurve([0,8169768624655967629114128598,0,-451787550647310420612086468536366715869054405951830599,0]);
MordellWeilShaInformation(E);
```

Sagemath returns $8$ for the upper bound of analytic rank, even for max_Delta=$3.3$ (we are still testing for higher max_Delta):

```
E = EllipticCurve([0,8169768624655967629114128598,0,-451787550647310420612086468536366715869054405951830599,0])
E.analytic_rank_upper_bound(max_Delta=3.3,root_number="compute")
```

Is there a way to find two more generators?

A similar question for the $6$ <= Rank(E) <= $7$ situation was successfully resolved by Jeremy Rouse (One more generator needed for a Z/6 elliptic curve) but our software chokes when we are trying to follow his instructions.

Max

TwoPowerIsogenyDescentRankBound(Fisher's code) prove at step 5 (just beyond 4-descent, but not yet 8-descent) the rank is at most 6 in about 20 seconds and 120 MB of memory? $\endgroup$ – MyNinthAccount Jan 31 at 4:44