An algorithm to compute volcanoes of 2-isogenies of elliptic curves over finite fields

The goal of this paper is presenting an algorithm to determine the structure of the volcano of 2-isogenies of a given elliptic curve over a finite field. The core of the algorithm relies on the relationship between the 2-torsion structure of the curves and its level in the volcano, as well as on those results that determine the direction of the different outgoing isogenies from each vertex. The algorithm is specially efficient for the so-called regular volcanoes, where the 2-torsion structure is different at every level.