Counting elliptic curves with prescribed torsion
Authors:
- 15 January 2015
- journal article
- research article
- Published by Walter de Gruyter GmbH in Journal für die reine und angewandte Mathematik (Crelles Journal)
- Vol. 2017 (729) , 151-170
Abstract
Mazur’s theorem states that there are exactly fifteen possibilities for the torsion subgroup of an elliptic curve over the rational numbers. We determine how often each of these groups actually occurs. Precisely, if G is one of these fifteen groups, we show that the number of elliptic curves up to height X whose torsion subgroup is isomorphic to G is on the order of X 1 / d {X^{1/d}} , for some number d = = d(G) which we compute.Keywords
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Funding Information
- National Science Foundation (DMS-1303082)
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