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Journal Articles Mathematics of Computation Year : 2005

Modular equations for hyperelliptic curves


We define modular equations describing the l-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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inria-00000627 , version 1 (10-11-2005)


  • HAL Id : inria-00000627 , version 1


Pierrick Gaudry, Eric Schost. Modular equations for hyperelliptic curves. Mathematics of Computation, 2005, 74, pp.429-454. ⟨inria-00000627⟩
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