Resumen de The effect of twisting on the 2-Selmer group

Peter Swinnerton-Dyer

• Let G be an elliptic curve defined over Q, all of whose 2-division points are rational, and let Gb be its quadratic twist by b. Subject to a mild additional condition on G, we find the limit of the probability distribution of the dimension of the 2-Selmer group of Gb as the number of prime factors of b increases; and we show that this distribution depends only on whether the 2-Selmer group of G has odd or even dimension.