Computation of Sets of Rational Points of Genus-3 Curves via the Dem'Janenko

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Computation of Sets of Rational Points of Genus-3 Curves via the Dem'Janenko–Manin Method

Published:2005 Issue: Volume:8 Page:267-300
ISSN:1461-1570
Container-title:LMS Journal of Computation and Mathematics
language:en
Short-container-title:LMS J. Comput. Math.

Author:

Girard Martine,Kulesz Leopoldo

Abstract

AbstractThe authors construct two families of genus-3 curves defined over Q(t) with three independent morphisms to an elliptic curve of rank at most two. They give explicit examples of an application of the Dem'janenko-Manin method that completely determines both the set of the Q(t)-rational points of the curves under consideration, and the set of Q-rational points of some specialisations.

Publisher

Wiley

Subject

Computational Theory and Mathematics,General Mathematics

Reference40 articles.

1. 40. Wetherell J.L. , ‘Bounding the number of rational points on certain curves of high rank’, Ph.D.thesis, University of California, Berkeley (1997).

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