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.

arXiv comment49 pages

References in corpus (6)

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