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

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.

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Item Permalink: https://hdl.handle.net/21.11116/0000-0004-396F-1 Version Permalink: https://hdl.handle.net/21.11116/0000-0004-3970-E
Genre: Journal Article

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Buhler, Joe P., Author
Gross, Benedict H.1, Author
Zagier, Don B.2, Author           
Affiliations:
1Max Planck Society, ou_persistent13              
2Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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 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.

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 Dates: 1985
 Publication Status: Issued
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: -
 Identifiers: eDoc: 744957
Other: 111
 Degree: -

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Title: Mathematics of Computation
Source Genre: Journal
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Publ. Info: American Mathematical Society, Providence, RI
Pages: - Volume / Issue: 44 Sequence Number: - Start / End Page: 473 - 481 Identifier: ISSN: 0025-5718