English

A Cohen-Lenstra phenomenon for elliptic curves

Number Theory 2014-02-13 v3

Abstract

Given an elliptic curve EE and a finite Abelian group GG, we consider the problem of counting the number of primes pp for which the group of points modulo pp is isomorphic to GG. 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.

Keywords

Cite

@article{arxiv.1206.1585,
  title  = {A Cohen-Lenstra phenomenon for elliptic curves},
  author = {Chantal David and Ethan Smith},
  journal= {arXiv preprint arXiv:1206.1585},
  year   = {2014}
}

Comments

A mistake was discovered in the derivation of the product formula for K(G). The included corrigendum corrects this mistake. All page numbers in the corrigendum refer to the journal version of the manuscript

R2 v1 2026-06-21T21:15:56.859Z