Section: New Software and Platforms

AVIsogenies

Participants : Damien Robert [correspondent] , Gaëtan Bisson, Romain Cosset [Inria project-team Caramel ] .

http://avisogenies.gforge.inria.fr/ .

AVIsogenies (Abelian Varieties and Isogenies) is a Magma package for working with abelian varieties, with a particular emphasis on explicit isogeny computation.

Its prominent feature is the computation of $(\ell ,\ell )$-isogenies between Jacobian varieties of genus-two hyperelliptic curves over finite fields of characteristic coprime to $\ell$; practical runs have used values of $\ell$ in the hundreds.

It can also be used to compute endomorphism rings of abelian surfaces, and find complete addition laws on them.

• Version: 0.6

• License: LGPL v2.1+

• Programming language: Magma