Isogeny volcanoes of elliptic curves and sylow subgroups

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Issue date
2015Suggested citation
Fouquet, Mireille;
Miret, Josep M. (Josep Maria);
Valera Martín, Javier;
.
(2015)
.
Isogeny volcanoes of elliptic curves and sylow subgroups.
Lecture Notes in Computer Science, 2015, vol. 8895.
https://doi.org/10.1007/978-3-319-16295-9_9.
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Given an ordinary elliptic curve over a finite field located in
the floor of its volcano of ℓ-isogenies, we present an efficient procedure
to take an ascending path from the floor to the level of stability and
back to the floor. As an application for regular volcanoes, we give an
algorithm to compute all the vertices of their craters. In order to do this,
we make use of the structure and generators of the ℓ-Sylow subgroups of
the elliptic curves in the volcanoes.