Abstract
| We describe theorems and computational methods for verifying the Birch and Swinnerton-Dyer conjecture for specific elliptic curves over Q. We apply our techniques to show that if E is a non-CM elliptic curve over Q of conductor ≤ 1000 and rank ≤ 1, then the full Birch and Swinnerton-Dyer conjecture is true for E up to odd primes that divide either a Tamagawa number of E or the degree of some rational cyclic isogeny with domain E. |
| DVI |
|---|
| LaTeX Source |
| Relevant Data, Tables, and Programs |