Open Access
2013 On the ranks of the $2$-Selmer groups of twists of a given elliptic curve
Daniel Kane
Algebra Number Theory 7(5): 1253-1279 (2013). DOI: 10.2140/ant.2013.7.1253


Swinnerton-Dyer considered the proportion of twists of an elliptic curve with full 2-torsion that have 2-Selmer group of a particular dimension. Swinnerton-Dyer obtained asymptotic results on the number of such twists using an unusual notion of asymptotic density. We build on this work to obtain similar results on the density of twists with particular rank of 2-Selmer group using the natural notion of density.


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Daniel Kane. "On the ranks of the $2$-Selmer groups of twists of a given elliptic curve." Algebra Number Theory 7 (5) 1253 - 1279, 2013.


Received: 27 June 2012; Revised: 4 January 2013; Accepted: 6 January 2013; Published: 2013
First available in Project Euclid: 20 December 2017

zbMATH: 1300.11061
MathSciNet: MR3101079
Digital Object Identifier: 10.2140/ant.2013.7.1253

Primary: 11G05

Keywords: Density , Elliptic curve , Selmer group

Rights: Copyright © 2013 Mathematical Sciences Publishers

Vol.7 • No. 5 • 2013
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