On the conjecture of Birch and Swinnerton-Dyer for an elliptic curve of rank
Authors:
Joe P. Buhler, Benedict H. Gross and Don B. Zagier
Journal:
Math. Comp. 44 (1985), 473-481
MSC:
Primary 11G40; Secondary 14G25
DOI:
https://doi.org/10.1090/S0025-5718-1985-0777279-X
MathSciNet review:
777279
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Abstract | References | Similar Articles | Additional Information
Abstract: The elliptic curve has rank 3 over Q. Assuming the Weil-Taniyama conjecture for this curve, we show that its L-series
has a triple zero at
and compute
to 28 decimal places; its value agrees with the product of the regulator and real period, in accordance with the Birch-Swinnerton-Dyer conjecture if III is trivial.
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Additional Information
DOI:
https://doi.org/10.1090/S0025-5718-1985-0777279-X
Article copyright:
© Copyright 1985
American Mathematical Society