Quadratic Twists as Random Variables

Abstract: If $E/\mathbb{Q}$ is an elliptic curve, and $d$ is a squarefree integer, then the $2$-torsion modules of $E$ and its quadratic twist $E_d$ are isomorphic. In particular their $2$-Selmer groups can be made to lie in the same space. Poonen-Rains provide a heuristic model for the behaviour of these $2$-Selmer groups individually, as E varies, but how independent are they? We'll present results in this direction.

number theory

Audience: researchers in the topic

London number theory seminar

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