Mathematics of Computation

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ISSN 1088-6842(e) ISSN 0025-5718(p)

Modular equations for hyperelliptic curves

Author(s): P. Gaudry; É. Schost.
Journal: Math. Comp. 74 (2005), 429-454.
MSC (2000): Primary 11Y40; Secondary 11G20, 11Y16
Posted: May 25, 2004
MathSciNet review: 2085901
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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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