On the ranks of the 2-Selmer groups of twists of a given elliptic curve
On the ranks of the 2-Selmer groups of twists of a given elliptic curve
In [8], 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 …