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arXiv · 1206.1585

A Cohen-Lenstra phenomenon for elliptic curves

Chantal David·Ethan Smith
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Abstract

Given an elliptic curve $E$ and a finite Abelian group $G$, we consider the problem of counting the number of primes $p$ for which the group of points modulo $p$ is isomorphic to $G$. Under a certain conjecture concerning the distribution of primes in short intervals, we obtain an asymptotic formula for this problem on average over a family of elliptic curves.

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Chantal David, Ethan Smith. 2014-02-11. A Cohen-Lenstra phenomenon for elliptic curves. https://doi.org/10.1112/jlms%2Fjdt036%3B%2010.1112%2Fjlms%2Fjdu001

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