A Cohen-Lenstra phenomenon for elliptic curves
Number Theory
2014-02-13 v3
Abstract
Given an elliptic curve and a finite Abelian group , we consider the problem of counting the number of primes for which the group of points modulo is isomorphic to . 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.
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