Chantal David, Ethan Smith
Published 2012-06-07, updated 2014-02-11Version 3
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.
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
Journal: Journal of the London Mathematical Society, 89(1):24-44, 2014; Corrigendum: Journal of the London Mathematical Society, 89(1):45-46, 2014
On the index of the Heegner subgroup of elliptic curves
Vanishing of L-functions of elliptic curves over number fields
Constructing families of elliptic curves with prescribed mod 3 representation via Hessian and Cayleyan curves
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