The average size of the 2-Selmer groups of elliptic curves
Abstract
We use the results of the previous talk. Developing a mass formula for the space of binary quartic forms, and using a squarefree sieve, we show that the average size of the 2-Selmer groups of elliptic curves is 3. This yields an upper bound of 1.5 on the average rank of elliptic curves. This is joint work with ManjulBhargava