On families of 9-congruent elliptic curves
Number Theory
2015-04-30 v1
Abstract
We compute equations for the families of elliptic curves 9-congruent to a given elliptic curve. We use these to find infinitely many non-trivial pairs of 9-congruent elliptic curves over Q, i.e. pairs of non-isogenous elliptic curves over Q whose 9-torsion subgroups are isomorphic as Galois modules.
Keywords
Cite
@article{arxiv.1504.07891,
title = {On families of 9-congruent elliptic curves},
author = {Tom Fisher},
journal= {arXiv preprint arXiv:1504.07891},
year = {2015}
}
Comments
18 pages. This article supersedes parts of arXiv:1105.1706