A majority of elliptic curves over $\mathbb Q$ satisfy the Birch and Swinnerton-Dyer conjecture

Abstract

We prove that a majority (in fact, $>66\%$) of all elliptic curves over $\mathbb Q$, when ordered by height, satisfy the Birch and Swinnerton-Dyer rank conjecture.

Some further details, clarifications, and references added; 17 pages