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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 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 order of Shafarevich--Tate groups, along with frustrating difficulties that have yet to be overcome.
This talk will be accessible to graduate students.
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