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arXiv · 1209.3085

Second p descents on elliptic curves

Brendan Creutz
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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.

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Brendan Creutz. 2012-09-14. Second p descents on elliptic curves. https://doi.org/10.1090/s0025-5718-2013-02713-5

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