Selmer companion curves
Number Theory
2012-08-21 v2
Abstract
We say that two elliptic curves E_1, E_2 over a number field K are n-Selmer companions for a positive integer n if for every quadratic character \chi of K, there is an isomorphism between the n-Selmer groups Sel_n(E_1^\chi/K) and Sel_n(E_2^\chi/K) of the quadratic twists E_1^\chi, E_2^\chi. We give sufficient conditions for two elliptic curves to be n-Selmer companions, and give a number of examples of non-isogenous pairs of companions.
Keywords
Cite
@article{arxiv.1203.0620,
title = {Selmer companion curves},
author = {Barry Mazur and Karl Rubin},
journal= {arXiv preprint arXiv:1203.0620},
year = {2012}
}
Comments
minor revisions