The Birch and Swinnerton-Dyer Formula for Elliptic Curves of Analytic Rank One

Dimitar Jetchev, Christopher Skinner, Xin Wan

Let $E/\mathbb{Q}$ be a semistable elliptic curve such that ${\mathrm{ord}}_{s=1}L(E,s)=1$. We prove the $p$-part of the Birch and Swinnerton-Dyer formula for $E/\mathbb{Q}$ for ea…