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On the conjecture of Birch and Swinnerton-Dyer for an elliptic curve of rank\quad 3.

MPS-Authors

Gross,  Benedict H.
Max Planck Society;

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Zagier,  Don B.
Max Planck Institute for Mathematics, Max Planck Society;

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Citation

Buhler, J. P., Gross, B. H., & Zagier, D. B. (1985). On the conjecture of Birch and Swinnerton-Dyer for an elliptic curve of rank\quad 3. Mathematics of Computation, 44, 473-481.


Cite as: http://hdl.handle.net/21.11116/0000-0004-396F-1
Abstract
The authors give numerical evidence for the Birch Swinnerton-Dyer conjecture for a particular Weil curve whose Mordell-Weil group has rank 3. For the Weil curves of rank lt;3 there is now very strong theoretical evidence for the Birch Swinnerton-Dyer conjecture, hence making a numerical investigation of a rank 3 curve very natural. The paper gives a very nice description of the mathematical preliminaries to the actual numerical calculation and ends by giving the numerical results which predict the Tate-Shafarevich group to be of order 1 up to 28 decimal places.