Descent via isogeny on elliptic curves with large rational torsion subgroups

Author: 

Flynn, E
Grattoni, C

Publication Date: 

1 April 2008

Journal: 

Journal of Symbolic Computation

Last Updated: 

2020-01-21T09:03:33.69+00:00

Issue: 

4

Volume: 

43

DOI: 

10.1016/j.jsc.2007.11.001

page: 

293-303

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. © 2007 Elsevier Ltd. All rights reserved.

Symplectic id: 

4262

Submitted to ORA: 

Not Submitted

Publication Type: 

Journal Article