Second p descents on elliptic curves
Number Theory
2015-12-18 v1
Abstract
Let p be a prime and let C be a genus one curve over a number field k representing an element of order dividing p in the Shafarevich-Tate group of its Jacobian. We describe an algorithm which computes the set of D in the Shafarevich-Tate group such that pD = C and obtains explicit models for these D as curves in projective space. This leads to a practical algorithm for performing 9-descents on elliptic curves over the rationals.
Cite
@article{arxiv.1209.3085,
title = {Second p descents on elliptic curves},
author = {Brendan Creutz},
journal= {arXiv preprint arXiv:1209.3085},
year = {2015}
}
Comments
45 pages