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

References in corpus (1)

• Indivisibility of Heegner points in the multiplicative case

Cited by in corpus (2)

• Indivisibility of Heegner points in the multiplicative case
• The average number of integral points on elliptic curves is bounded