The Mathematical Institute, University of Oxford, Eprints Archive

Descent Via Isogeny on Elliptic Curves with Large Rational Torsion Subgroups.

Flynn, E. V. and Grattoni, C. (2008) Descent Via Isogeny on Elliptic Curves with Large Rational Torsion Subgroups. Journal of Symbolic Computation, 43 . pp. 293-303. ISSN 0747-7171

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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.

Item Type:Article
Subjects:H - N > Number theory
Research Groups:Number Theory Group
ID Code:800
Deposited By:E. Victor Flynn
Deposited On:01 Sep 2009 08:34
Last Modified:01 Sep 2009 08:34

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