Proving the Birch and Swinnerton-Dyer conjecture for specific elliptic curves of analytic rank zero and one

Details Proving the Birch and Swinnerton-Dyer conjecture for specific elliptic curves of analytic rank zero and one Proving the Birch and Swinnerton-Dyer conjecture for specific elliptic curves of analytic rank zero and one

2010-10-12

arxiv.org/abs/1010.2431v3

LMS J. Comput. Math. 14 (2011) 327-350

Mathematics

Number Theory

25 pages, 9 tables

Scientific paper

We describe an algorithm to prove the Birch and Swinnerton-Dyer conjectural
formula for any given elliptic curve defined over the rational numbers of
analytic rank zero or one. With computer assistance we have proved the formula
for 16714 of the 16725 such curves of conductor less than 5000.

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