Three-descent and the Birch and Swinnerton-Dyer conjecture. (English) Zbl 1083.11040

Bandini, Andrea

Rocky Mt. J. Math. 34, No. 1, 13-27 (2004).

The first part of this article explains how to perform a simple \(3\)-descent on elliptic curves of the form \(y^2 = x^3 + a\), based on the expositions of P. Satgé [J. Number Theory 23, 294–317 (1986; Zbl 0601.14027)] and J. Top [The proceedings of the third conference of the Canadian Number Theory Association, held at Queen’s University, Kingston, Canada, August 18–24, 1991. Oxford: Clarendon Press, 303–317 (1993; Zbl 0804.11040)]. The second part gives numerical results and verifies the conjecture of Birch and Swinnerton-Dyer for some specific examples.

Reviewer: Franz Lemmermeyer (Bilkent)

MSC:

11G40

\(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture

Keywords:

elliptic curves; 3-descent; Tate-Shafarevich group; Birch and Swinnerton-Dyer conjecture

Citations:

Zbl 0601.14027; Zbl 0804.11040

References:

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