The Birch and Swinnerton-Dyer Conjecture: A brief survey

Abstract

The celebrated Birch and Swinnerton-Dyer (BSD) conjecture connects the structure of the rational points on an elliptic curve defined over the rationals to the analytic properties of its associated Hasse–Weil L L -function. In this paper we recall the BSD conjecture (and its various parts) and survey some of the known results towards it, especially recent work.