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arXiv · 2512.23921

The probability of isomorphic group structures of isogenous elliptic curves over finite fields

John Cullinan·Nathan Kaplan
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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}.

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John Cullinan, Nathan Kaplan. 2025-12-30. The probability of isomorphic group structures of isogenous elliptic curves over finite fields. https://arxiv.org/abs/2512.23921

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