A majority of elliptic curves over $\mathbb Q$ satisfy the Birch and   Swinnerton-Dyer conjecture
  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. 
Manjul Bhargava, Christopher Skinner, and Wei Zhang
math.NT