The second moment of the size of the 2-Selmer group of elliptic curves
The second moment of the size of the 2-Selmer group of elliptic curves
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Ashvin Swaminathan, Princeton University
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We introduce a new orbit parametrization for square roots of听the class of the inverse different in rings cut out by binary forms. This听parametrization has many applications of interest in arithmetic statistics;听for example, we use it to prove that the second moment of the size of the听2-Selmer group of elliptic curves is at most 15, confirming a conjecture of听Poonen and Rains.