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

MathSciNet review:
777279

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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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DOI:
http://dx.doi.org/10.1090/S0025-5718-1985-0777279-X

Article copyright:
© Copyright 1985
American Mathematical Society