On the Ranks of the 2-Selmer Groups of Twists of a Given Elliptic Curve

Abstract

We extend work of Swinnerton-Dyer on the density of the number of twists of a given elliptic curve that have 2-Selmer group of a particular rank.

References in corpus (2)

• Ranks of twists of elliptic curves and Hilbert's Tenth Problem
• Disparity in Selmer ranks of quadratic twists of elliptic curves

Cited by in corpus (7)

• Disparity in Selmer ranks of quadratic twists of elliptic curves
• The average size of the 3-isogeny Selmer groups of elliptic curves $y^2=x^3+k$
• A Markov model for Selmer ranks in families of twists
• Three-isogeny Selmer groups and ranks of abelian varieties in quadratic twist families over a number field
• On 2-Selmer groups of twists after quadratic extension
• The distribution of 2-Selmer ranks of quadratic twists of elliptic curves with partial two-torsion
• The $3$-isogeny Selmer groups of the elliptic curves $y^2=x^3+n^2$