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

Published online by Cambridge University Press:  01 February 2010

Martine Girard  and
Leopoldo Kulesz
Martine Girard
Affiliation:
School of Mathematics and Statistics, University of Sydney NSW 2006, Australia, girard@maths.usyd.edu.au, http://www.maths.usyd.edu.au/u/girard/
Leopoldo Kulesz
Affiliation:
Instituto de Desarollo Humano, Universidad National de General Sarmiento, Roca 850 San Miguel, Pcia. de Buenos Aires. 1663, Argentina, lk@delzorzal.com.ar

Abstract

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The 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.

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 8 , 2005 , pp. 267 - 300
Copyright
Copyright © London Mathematical Society 2005

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