Computing low-degree isogenies in genus 2 with the Dolgachev-Lehavi method

Benjamin Smith 1
1 TANC - Algorithmic number theory for cryptology
LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau], Inria Saclay - Ile de France
Abstract : Let ell be a prime, and H a curve of genus 2 over a field k of characteristic not 2 or ell. If S is a maximal Weil-isotropic subgroup of Jac(H)[ell], then Jac(H)/S is isomorphic to the Jacobian of some (possibly reducible) curve X. We investigate the Dolgachev--Lehavi method for constructing the curve X, simplifying their approach and making it more explicit. The result, at least for ell=3, is an efficient and easily programmable algorithm suitable for number-theoretic calculations.
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https://hal.inria.fr/inria-00632118
Contributor : Benjamin Smith <>
Submitted on : Thursday, October 13, 2011 - 3:05:08 PM
Last modification on : Wednesday, March 27, 2019 - 4:41:29 PM
Long-term archiving on : Saturday, January 14, 2012 - 2:27:50 AM

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  • HAL Id : inria-00632118, version 1
  • ARXIV : 1110.2963

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Benjamin Smith. Computing low-degree isogenies in genus 2 with the Dolgachev-Lehavi method. 2011. ⟨inria-00632118v1⟩

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