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

TL;DR

This paper proves that over 66% of elliptic curves over the rationals, ordered by height, satisfy the Birch and Swinnerton-Dyer conjecture regarding their rank, providing significant statistical evidence for the conjecture.

Contribution

It establishes that a majority of elliptic curves over ield satisfy the BSD conjecture, a result previously unconfirmed on such a large scale.

Findings

Over 66% of elliptic curves satisfy BSD conjecture

Results are based on ordering curves by height

Provides statistical support for BSD 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.