# Math 583e -- Computational Number Theory (part 2)

- MWF at 1:30pm in MEB 243
Course Notes for Modular Abelian Varieties part of the course: modabvar.pdf

Professors: William Stein and Bill Hart

- Topics:
- Integer factorization
- Modular abelian varieties

Google group mailing list: http://groups.google.com/group/583-uw09

- Grading: Your grade will be based entirely on 2 projects, one on integer factorization (due April 27), and one on modular abelian varieties (due June 5). There will be no graded homework.
- References:
Rough notes in progress for this part of the course [linked pdf] (Stein)

Algorithms for Modular Elliptic Curves (Cremona)

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

An introduction to computing modular forms using modular symbols (Stein)

The Manin Constant (Agashe, Ribet, Stein)

Visible Evidence for the Birch and Swinnerton-Dyer Conjecture for Rank 0 Modular Abelian Varieties (Agashe-Stein)

Visibility of Shafarevich-Tate Groups of Abelian Varieties (Agashe-Stein)

Component Groups of Purely Toric Quotients of Semistable Jacobians (Conrad-Stein)

Osserman's MIT student reading seminar from 2001 on Kolyvagin's Euler System