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Modular equations for hyperelliptic curves |
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| Authors: | P. Gaudry É . Schost. |
| Affiliation: | Laboratoire LIX, École polytechnique, 91128 Palaiseau, France ; Laboratoire STIX, École polytechnique, 91128 Palaiseau, France |
| Abstract: | We define modular equations describing the  -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. |
| Keywords: | Modular equations hyperelliptic curves Schoof-Elkies-Atkin algorithm |
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