Skip to Main Content

Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2024 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Modular equations for hyperelliptic curves
HTML articles powered by AMS MathViewer

by P. Gaudry and É. Schost;
Math. Comp. 74 (2005), 429-454
DOI: https://doi.org/10.1090/S0025-5718-04-01682-5
Published electronically: May 25, 2004

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.
References
Similar Articles
  • Retrieve articles in Mathematics of Computation with MSC (2000): 11Y40, 11G20, 11Y16
  • Retrieve articles in all journals with MSC (2000): 11Y40, 11G20, 11Y16
Bibliographic 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
  • Received by editor(s): July 15, 2002
  • Received by editor(s) in revised form: August 16, 2003
  • Published electronically: May 25, 2004
  • © Copyright 2004 Copyright held by the authors
  • Journal: Math. Comp. 74 (2005), 429-454
  • MSC (2000): Primary 11Y40; Secondary 11G20, 11Y16
  • DOI: https://doi.org/10.1090/S0025-5718-04-01682-5
  • MathSciNet review: 2085901