Three-descent and the Birch and Swinnerton-Dyer conjecture (Q1880963)

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 \textit{P. Satgé} [J. Number Theory 23, 294--317 (1986; Zbl 0601.14027)] and \textit{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.