Skip to Main Content

Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Computing $(\ell ,\ell )$-isogenies in polynomial time on Jacobians of genus $2$ curves
HTML articles powered by AMS MathViewer

by Romain Cosset and Damien Robert PDF
Math. Comp. 84 (2015), 1953-1975 Request permission


In this paper, we compute $\ell$-isogenies between abelian varieties over a field of characteristic different from $2$ in polynomial time in $\ell$, when $\ell$ is an odd prime which is coprime to the characteristic. We use level $n$ symmetric theta structure where $n=2$ or $n=4$. In the second part of this paper we explain how to convert between Mumford coordinates of Jacobians of genus $2$ hyperelliptic curves to theta coordinates of level $2$ or $4$. Combined with the preceding algorithm, this gives a method to compute $(\ell ,\ell )$-isogenies in polynomial time on Jacobians of genus $2$ curves.
Similar Articles
Additional Information
  • Romain Cosset
  • Affiliation: Campus Scientifique, Loria, 54506 Vandouevre-Les-Nancy, France
  • Email:
  • Damien Robert
  • Affiliation: Universite Bordeaux 1, Institut Mathematiques de Bordeaux, 351 Cours de la Liberation, Batiment A33, 33405 Talence, Cedex France
  • Email:
  • Received by editor(s): March 24, 2011
  • Received by editor(s) in revised form: October 4, 2013
  • Published electronically: November 18, 2014
  • © Copyright 2014 American Mathematical Society
  • Journal: Math. Comp. 84 (2015), 1953-1975
  • MSC (2010): Primary 11Y40, 14K02; Secondary 94A60, 14G50, 11T71
  • DOI:
  • MathSciNet review: 3335899