Section: Software

AVIsogenies

Participants : Gaëtan Bisson [contact] , Romain Cosset.

AVIsogenies (Abelian Varieties and Isogenies) is a Magma package for working with abelian varieties, with a particular emphasis on explicit isogeny computation; it has been publicly released under the LGPLv2+ license in 2010.

Its prominent feature is the computation of $(\ell ,\ell )$-isogenies between Jacobian varieties of genus-2 hyperelliptic curves over finite fields; practical runs have involved values of $\ell$ in the hundreds. It also provides procedures for exploring and drawing isogeny graphs, and for computing various complex-multiplication-related structures, such as Shimura's gothic C group.

In 2011, two incremental versions have been released. They provide the following new features: the characteristic 2 is now supported, and the complete addition laws of [23] have been implemented.

The package can be obtained at http://avisogenies.gforge.inria.fr/ .