Explicit isogeny descent on elliptic curves
نویسندگان
چکیده
منابع مشابه
Explicit isogeny descent on elliptic curves
In this note, we consider an `-isogeny descent on a pair of elliptic curves over Q. We assume that ` > 3 is a prime. The main result expresses the relevant Selmer groups as kernels of simple explicit maps between finitedimensional F`-vector spaces defined in terms of the splitting fields of the kernels of the two isogenies. We give examples of proving the `-part of the Birch and Swinnerton-Dyer...
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This is the second in a series of papers in which we study the n-Selmer group of an elliptic curve. In this paper, we show how to realize elements of the n-Selmer group explicitly as curves of degree n embedded in Pn−1. The main tool we use is a comparison between an easily obtained embedding into Pn2−1 and another map into Pn2−1 that factors through the Segre embedding Pn−1×Pn−1 → Pn2−1. The c...
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This is the third in a series of papers in which we study the n-Selmer group of an elliptic curve, with the aim of representing its elements as curves of degree n in Pn−1. The methods we describe are practical in the case n = 3 for elliptic curves over the rationals, and have been implemented in MAGMA. One important ingredient of our work is an algorithm for trivialising central simple algebras...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2012
ISSN: 0025-5718,1088-6842
DOI: 10.1090/s0025-5718-2012-02619-6