Vol. 1, No. 1, 2013

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Fast computation of isomorphisms of hyperelliptic curves and explicit Galois descent

Reynald Lercier, Christophe Ritzenthaler and Jeroen Sijsling

Vol. 1 (2013), No. 1, 463–486
Abstract

We show how to speed up the computation of isomorphisms of hyperelliptic curves by using covariants. We also obtain new theoretical and practical results concerning models of these curves over their field of moduli.

Keywords
invariants, covariants, hyperelliptic curves, binary forms, Galois descent, isomorphism, moduli, algorithm
Mathematical Subject Classification 2010
Primary: 13A50
Secondary: 14Q05, 14H10, 14H25
Milestones
Accepted: 2 October 2013
Published: 14 November 2013
Authors
Reynald Lercier
DGA MI
La Roche Marguerite
35174 Bruz
France
Laboratoire IRMAR
Université de Rennes 1
Campus de Beaulieu
35042 Rennes
France
Christophe Ritzenthaler
Institut de Mathématiques de Luminy
UMR 6206 du CNRS
Luminy, Case 907
13288 Marseille
France
Laboratoire IRMAR, UMR CNRS 6625
Campus de Beaulieu
35042 Rennes
France
Jeroen Sijsling
Laboratoire IRMAR
Université de Rennes 1
Campus de Beaulieu
35042 Rennes
France
Mathematics Institute
Zeeman Building
University of Warwick
Coventry CV4 7AL
United Kingdom