Volcanoes of l-isogenies of elliptic curves over finite fields: The case l=3.

Miret Biosca, Josep M., et al. "Volcanoes of l-isogenies of elliptic curves over finite fields: The case l=3.." Publicacions Matemàtiques 51.Extra (2007): 165-180. <http://eudml.org/doc/41920>.

@article{MiretBiosca2007,
abstract = {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)].},
author = {Miret Biosca, Josep M., Sadornil Renedo, Daniel, Tena Ayuso, Juan, Tomàs, Rosana, Valls Marsal, Magda},
journal = {Publicacions Matemàtiques},
keywords = {Teoría de números; Curvas elípticas; Campos finitos; Geometría diofántica; elliptic curves; finite fields; isogenies; volcanoes; Sylow subgroup; algorithms},
language = {eng},
number = {Extra},
pages = {165-180},
title = {Volcanoes of l-isogenies of elliptic curves over finite fields: The case l=3.},
url = {http://eudml.org/doc/41920},
volume = {51},
year = {2007},
}

TY - JOUR
AU - Miret Biosca, Josep M.
AU - Sadornil Renedo, Daniel
AU - Tena Ayuso, Juan
AU - Tomàs, Rosana
AU - Valls Marsal, Magda
TI - Volcanoes of l-isogenies of elliptic curves over finite fields: The case l=3.
JO - Publicacions Matemàtiques
PY - 2007
VL - 51
IS - Extra
SP - 165
EP - 180
AB - 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)].
LA - eng
KW - Teoría de números; Curvas elípticas; Campos finitos; Geometría diofántica; elliptic curves; finite fields; isogenies; volcanoes; Sylow subgroup; algorithms
UR - http://eudml.org/doc/41920
ER -