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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Modular equations for hyperelliptic curves


Authors: P. Gaudry and É. Schost
Journal: Math. Comp. 74 (2005), 429-454
MSC (2000): Primary 11Y40; Secondary 11G20, 11Y16
Published electronically: May 25, 2004
MathSciNet review: 2085901
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Abstract | References | Similar Articles | Additional Information

Abstract: We define modular equations describing the $\ell$-torsion subgroups of the Jacobian of a hyperelliptic curve. Over a finite base field, we prove factorization properties that extend the well-known results used in Atkin's improvement of Schoof's genus 1 point counting algorithm.


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Additional Information

P. Gaudry
Affiliation: Laboratoire LIX, École polytechnique, 91128 Palaiseau, France
Email: gaudry@lix.polytechnique.fr

É. Schost
Affiliation: Laboratoire STIX, École polytechnique, 91128 Palaiseau, France
Email: schost@stix.polytechnique.fr

DOI: http://dx.doi.org/10.1090/S0025-5718-04-01682-5
PII: S 0025-5718(04)01682-5
Keywords: Modular equations, hyperelliptic curves, Schoof-Elkies-Atkin algorithm
Received by editor(s): July 15, 2002
Received by editor(s) in revised form: August 16, 2003
Published electronically: May 25, 2004
Article copyright: © Copyright 2004 Copyright held by the authors