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A Cohen–Lenstra phenomenon for elliptic curves
Author(s) -
David Chantal,
Smith Ethan
Publication year - 2014
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdt036
Subject(s) - mathematics , elliptic curve , modulo , supersingular elliptic curve , abelian group , sato–tate conjecture , conjecture , modular elliptic curve , distribution (mathematics) , schoof's algorithm , pure mathematics , combinatorics , discrete mathematics , mathematical analysis , quarter period
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.