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A Cohen-Lenstra phenomenon for elliptic curves
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classification
math.NT
keywords
ellipticcurvesgroupprimesproblemabelianasymptoticaverage
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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