Studying the Birch and Swinnerton-Dyer Conjecture for Modular Abelian Varieties Using MAGMA

William A. Stein

Department of Mathematics, Harvard University

In this paper we describe the Birch and Swinnerton-Dyer conjecture about modular abelian varieties and how to use MAGMA to do computations with the quantities that appear in the conjecture. We assume the reader has some experience with algebraic varieties and number theory, but do not assume the reader has proficiency working with elliptic curves, abelian varieties, modular forms, or modular symbols.