On families of n-congruent elliptic curves
Number Theory
2011-05-10 v1
Abstract
We use an invariant-theoretic method to compute certain twists of the modular curves X(n) for n=7,9,11. Searching for rational points on these twists enables us to find non-trivial pairs of n-congruent elliptic curves over Q, i.e. pairs of non-isogenous elliptic curves over Q whose n-torsion subgroups are isomorphic as Galois modules. We also show by giving explicit non-trivial examples over Q(T) that there are infinitely many examples over Q in the cases n=9 and n=11.
Cite
@article{arxiv.1105.1706,
title = {On families of n-congruent elliptic curves},
author = {Tom Fisher},
journal= {arXiv preprint arXiv:1105.1706},
year = {2011}
}
Comments
57 pages