Two-cover descent on hyperelliptic curves-Reference-Cited by-同舟云学术

Two-cover descent on hyperelliptic curves

Published:2009-03-11 Issue:268 Volume:78 Page:2347-2370
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Bruin Nils,Stoll Michael

Abstract

We describe an algorithm that determines a set of unramified covers of a given hyperelliptic curve, with the property that any rational point will lift to one of the covers. In particular, if the algorithm returns an empty set, then the hyperelliptic curve has no rational points. This provides a relatively efficiently tested criterion for solvability of hyperelliptic curves. We also discuss applications of this algorithm to curves of genus 1 1 and to curves with rational points.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/2009-78-268/S0025-5718-09-02255-8/S0025-5718-09-02255-8.pdf

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4. Some ternary Diophantine equations of signature (𝑛,𝑛,2);Bruin, Nils,2006

5. Trinomials 𝑎𝑥⁷+𝑏𝑥+𝑐 and 𝑎𝑥⁸+𝑏𝑥+𝑐 with Galois groups of order 168 and 8⋅168;Bruin, Nils,2002

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