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
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.
|Subjects:||H - N > Number theory|
|Research Groups:||Number Theory Group|
|Deposited By:||E. Victor Flynn|
|Deposited On:||01 Sep 2009 07:34|
|Last Modified:||29 May 2015 18:29|
Repository Staff Only: item control page