Studying the Birch and Swinnerton-Dyer conjecture for modular abelian varieties using Magma.

In this paper we describe the Birch and Swinnerton-Dyer conjecture in the case of modular abelian varieties and how to use Magma to do computations with some of 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. The computations give evidence for the Birch and Swinnerton- Dyer conjecture and increase our explicit understanding of modular abelian varieties. [ABSTRACT FROM AUTHOR]