1 | initial version |
The reason why this curve is a little problematic is because it has nontrivial Sha[2]. It would be fairly straightforward to get E.gens()
to work: this is a rank 1 elliptic curve and enough of BSD is proved that this can be proven analytically. Sage knows how to do that too:
sage: E.rank(only_use_mwrank=False,proof=True)
1
So the only thing to do is to prove that the point you found isn't divisible by any $n>1$. It is a little surprising that E.gens
doesn't seem to have obvious options to help it discover this. The basic elements for implementing this are available.