Computing low-degree isogenies in genus 2 with the Dolgachev-Lehavi method - Archive ouverte HAL Access content directly
Journal Articles Contemporary mathematics Year : 2012

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

(1)
1

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.
Fichier principal
Vignette du fichier
isogenies.pdf (134.67 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

inria-00632118 , version 1 (13-10-2011)
inria-00632118 , version 2 (25-01-2012)

Identifiers

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

Cite

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

Altmetric

Share

Gmail Facebook Twitter LinkedIn More