English

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}.

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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}
}

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11 pages