The second moment of the size of the $2$-Selmer group of elliptic curves

Abstract

In this paper, we prove that when elliptic curves over $\mathbb{Q}$ are ordered by height, the second moment of the size of the $2$-Selmer group is at most $15$. This confirms a conjecture of Poonen and Rains.

49 pages

References in corpus (2)

• Two-cover descent on hyperelliptic curves
• The average size of the 2-Selmer group of Jacobians of hyperelliptic curves having a rational Weierstrass point