We survey algorithms for computing isogenies between elliptic curves defined over a field of characteristic either 0 or a large prime. We introduce a new algorithm that computes an isogeny of degree l (l different fro...
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We survey algorithms for computing isogenies between elliptic curves defined over a field of characteristic either 0 or a large prime. We introduce a new algorithm that computes an isogeny of degree l (l different from the characteristic) in time quasi-linear with respect to l. This is based in particular on fast algorithms for power series expansion of the Weierstrass P-function and related functions.
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'...
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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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