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- W2971148876 abstract "We present a quasi-linear algorithm to compute (separable) isogenies of degree $ell ^g$, for $ell$ an odd prime number, between Jacobians of curves of genus $g=2$ and $3$ starting from the equation of the curve $mathcal {C}$ and a maximal isotropic subgroup $mathcal {V}$ of the $ell$-torsion, generalizing Véluâs formula from genus $1$. Denoting by $J_{mathcal {C}}$ the Jacobian of $mathcal {C}$, the isogeny is $J_{mathcal {C}}to J_{mathcal {C}}/mathcal {V}$. Thus $mathcal {V}$ is the kernel of the isogeny and we compute only isogenies with such kernels. This work is based on the paper Computing functions on Jacobians and their quotients of Jean-Marc Couveignes and Tony Ezome. We improve their genus $2$ algorithm, generalize it to genus $3$ hyperelliptic curves, and introduce a way to deal with the genus $3$ nonhyperelliptic case, using algebraic theta functions." @default.
- W2971148876 created "2019-09-05" @default.
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- W2971148876 date "2019-10-28" @default.
- W2971148876 modified "2023-09-23" @default.
- W2971148876 title "Computing isogenies between Jacobians of curves of genus 2 and 3" @default.
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- W2971148876 doi "https://doi.org/10.1090/mcom/3486" @default.
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