Computing the Selmer group of an isogeny between Abelian varieties using a further isogeny to a Jacobian

摘要

This article describes an algorithm for computing the Selmer group of an isogeny between abelian varieties. This algorithm applies when there is an isogeny from the image abelian variety to the Jacobian of a curve. The use of an auxiliary Jacobian simplifies the determination of locally trivial cohomology classes. An example is presented where the rational solutions to x(4) + (y(2) + 1)(x + y) = 0 are determined. (c) 2005 Elsevier Inc. All rights reserved.