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

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 metadatas

Cited literature [12 references]  Display  Hide  Download

https://hal.inria.fr/inria-00632118
Contributor : Benjamin Smith <>
Submitted on : Wednesday, January 25, 2012 - 12:58:32 PM
Last modification on : Wednesday, November 29, 2017 - 3:51:59 PM
Long-term archiving on : Thursday, April 26, 2012 - 2:26:41 AM

Files

isogenies.pdf
Files produced by the author(s)

Identifiers

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

Collections

Citation

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⟩

Share

Metrics

Record views

330

Files downloads

247