Second p descents on elliptic curves

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.

45 pages

References in corpus (3)

• Two-cover descent on hyperelliptic curves
• Explicit n-descent on elliptic curves. III. Algorithms
• Second Isogeny Descents and the Birch and Swinnerton-Dyer Conjectural Formula

Cited by in corpus (1)

• Second Isogeny Descents and the Birch and Swinnerton-Dyer Conjectural Formula