On Isomorphic K-rational Groups of Isogenous Elliptic Curves over Finite Fields
Number Theory
2020-11-26 v2
Abstract
We show that two ordinary isogenous elliptic curves have isomorphic groups of rational points if they have the same -invariant and we extend this result to certain isogenous supersingular elliptic curves, namely those with equal -invariant of either 0 or 1728. Using a result by Heuberger and Mazzoli we establish a general case of this relationship within isogenous elliptic curves not necessarily having equal -invariant.
Cite
@article{arxiv.2011.08471,
title = {On Isomorphic K-rational Groups of Isogenous Elliptic Curves over Finite Fields},
author = {Liljana Babinkostova and Andrew Gao and Ben Kuehnert and Geneva Schlafly and Zecheng Yi},
journal= {arXiv preprint arXiv:2011.08471},
year = {2020}
}
Comments
15 pages, 1 figure