Joint IAS/Princeton University Number Theory Seminar

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