Volcanoes of l-isogenies of elliptic curves over finite fields: the case l=3
Sadornil Renedo, Daniel
Tena Ayuso, Juan
Tomàs Cuñat, Rosa Ana
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This paper is devoted to the study of the volcanoes of l-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 l-Sylow subgroup of an elliptic curve and
the level of the volcano where it is placed. The particular case l = 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.