Revistes Catalanes amb Accés Obert (RACO)

Volcanoes of $\ell$-isogenies of elliptic curves

J. M. Miret, D. Sadornil, J. Tena, R. Tomàs, M. Valls


This paper is devoted to the study of the volcanoes of $\ell$-isogenies of elliptic curves over a finite field, focusing on their height as well as on the location of curves across its different levels. The core of the paper lies on the relationship
between the $\ell$-Sylow subgroup of an elliptic curve and the level of
the volcano where it is placed. The particular case $\ell=3$ is studied in detail, giving an algorithm to determine the volcano of $3$-isogenies of a given
elliptic curve. Experimental results are also provided.

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