The probability of isomorphic group structures of isogenous elliptic curves over finite fields
Number Theory
2026-01-01 v1
Abstract
Let l be a prime number and let E and E' be l-isogenous elliptic curves defined over Q. In this paper we determine the proportion of primes p for which E(F_p) is isomorphic to E'(F_p). Our techniques are based on those developed in \cite{ck} and \cite{rnt}.
Cite
@article{arxiv.2512.23921,
title = {The probability of isomorphic group structures of isogenous elliptic curves over finite fields},
author = {John Cullinan and Nathan Kaplan},
journal= {arXiv preprint arXiv:2512.23921},
year = {2026}
}
Comments
11 pages