English

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.

Keywords

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

R2 v1 2026-06-21T22:04:50.620Z