I am trying to find the next rank 8 curve with the torsion subgroup Z/6 using Kihara's family as described in https://arxiv.org/pdf/1503.03667.pdf. Meanwhile, I came across a curve generated by $t=629/3287$ (or $t=6202/8089$, $t=-8089/1772$, $t=-23009/1258$).

Magma Calculator (http://magma.maths.usyd.edu.au/calc/) and mwrank return 6 generators for this curve.

```
SetClassGroupBounds("GRH");
E := EllipticCurve([1, 0, 1, -134523401167995213138670219183146040563810987418811883, 66402369909929526433604564866758135700820111823876373971833120805994125518227306]);
MordellWeilShaInformation(E);
```

Sagemath 8.4 returns 7 for the upper bound of analytic rank.

```
E = EllipticCurve([1,0,1,-134523401167995213138670219183146040563810987418811883,66402369909929526433604564866758135700820111823876373971833120805994125518227306])
E.analytic_rank_upper_bound(max_Delta=2.8,root_number="compute")
```

Is there a way to find one more generator?

A working piece of any code would be greatly appreciated.

Max