Article ID Journal Published Year Pages File Type
401916 Journal of Symbolic Computation 2008 11 Pages PDF
Abstract

We outline PARI programs which assist with various algorithms related to descent via isogeny on elliptic curves. We describe, in this context, variations of standard inequalities which aid the computation of members of the Tate–Shafarevich group. We apply these techniques to several examples: in one case we use descent via 9-isogeny to determine the rank of an elliptic curve; in another case we find nontrivial members of the 9-part of the Tate–Shafarevich group, and in a further case, nontrivial members of the 13-part of the Tate–Shafarevich group.

Related Topics
Physical Sciences and Engineering Computer Science Artificial Intelligence