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Elliptic curves of rank 1 satisfying the 3-part of the Birch and Swinnerton–Dyer conjecture
- Source :
-
Journal of Number Theory . Dec2010, Vol. 130 Issue 12, p2707-2714. 8p. - Publication Year :
- 2010
-
Abstract
- Abstract: Let E be an elliptic curve over of conductor N and K be an imaginary quadratic field, where all prime divisors of N split. If the analytic rank of E over K is equal to 1, then the Gross and Zagier formula for the value of the derivative of the L-function of E over K, when combined with the Birch and Swinnerton–Dyer conjecture, gives a conjectural formula for the order of the Shafarevich–Tate group of E over K. In this paper, we show that there are infinitely many elliptic curves E such that for a positive proportion of imaginary quadratic fields K, the 3-part of the conjectural formula is true. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 0022314X
- Volume :
- 130
- Issue :
- 12
- Database :
- Academic Search Index
- Journal :
- Journal of Number Theory
- Publication Type :
- Academic Journal
- Accession number :
- 53430132
- Full Text :
- https://doi.org/10.1016/j.jnt.2010.07.001