Skip to Main content Skip to Navigation
Journal articles

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

Benjamin Smith 1
1 GRACE - Geometry, arithmetic, algorithms, codes and encryption
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.
Document type :
Journal articles
Complete list of metadata

Cited literature [12 references]  Display  Hide  Download
Contributor : Benjamin Smith Connect in order to contact the contributor
Submitted on : Wednesday, January 25, 2012 - 12:58:32 PM
Last modification on : Thursday, January 20, 2022 - 4:15:31 PM
Long-term archiving on: : Thursday, April 26, 2012 - 2:26:41 AM


Files produced by the author(s)


  • HAL Id : inria-00632118, version 2
  • ARXIV : 1110.2963



Benjamin Smith. Computing low-degree isogenies in genus 2 with the Dolgachev-Lehavi method. Contemporary mathematics, American Mathematical Society, 2012, Arithmetic, Geometry, Cryptography and Coding Theory, 574, pp.159-170. ⟨inria-00632118v2⟩



Les métriques sont temporairement indisponibles