Section: New Software and Platforms

AVIsogenies

Abelian Varieties and Isogenies

Functional Description

AVIsogenies is a Magma package for working with abelian varieties, with a particular emphasis on explicit isogeny computation.

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

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

• Participants: Gaëtan Bisson, Romain Cosset and Damien Robert

• Contact: Damien Robert

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