Quadratic twist families of elliptic curves with unusual $2^{\infty }$-Selmer groups
Apparaît dans la collection : Jean-Morlet Chair - Conference - Arithmetic Statistics / Chaire Jean-Morlet - Conférence - Statistiques arithmétiques
Given any elliptic curve $E$ over the rationals, we show that 50 % of the quadratic twists of $E$ have $2^{\infty}$-Selmer corank 0 and 50 % have $2^{\infty}$-Selmer corank 1. As a result, we show that Goldfeld's conjecture follows from the Birch and Swinnerton-Dyer conjecture.
