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 aIso provided.
[Proceedings of the Primeras Jornadas de Teoría de Números (Vilanova i la Geltrú (Barcelona), 30 June - 2 July 2005)].
@article{urn:eudml:doc:41920,
title = {Volcanoes of l-isogenies of elliptic curves over finite fields: The case l=3.},
journal = {Publicacions Matem\`atiques},
year = {2007},
pages = {165-180},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41920}
}
Miret Biosca, Josep M.; Sadornil Renedo, Daniel; Tena Ayuso, Juan; Tomàs, Rosana; Valls Marsal, Magda. Volcanoes of l-isogenies of elliptic curves over finite fields: The case l=3.. Publicacions Matemàtiques, (2007), pp. 165-180. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41920/