##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory

## William Stein

#### Harvard University

## Computational verification of the full Birch and Swinnerton-Dyer conjecture for specific elliptic curves

##### Abstract:

This talk is about a long-term project to verify the full Birch and Swinnerton-Dyer conjecture for every elliptic curve in Cremona's book, except the $18$ optimal curves of rank $2$. The methods involve Kolyvagin's Euler system of Heegner points, computation, and whatever else one can use. I'll begin with a discussion of the Birch and Swinnerton-Dyer conjecture for elliptic curves, and methods for computing the true order of Shafarevich-Tate groups, along with frustrating difficulties that have yet to be overcome.

Host: Efim Zelmanov

### February 1, 2005

### 3:00 PM

### AP&M 5829

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