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

Josep M. Miret Biosca; Daniel Sadornil Renedo; Juan Tena Ayuso; Rosana Tomàs; Magda Valls Marsal

Publicacions Matemàtiques (2007)

- Volume: 51, Issue: Extra, page 165-180
- ISSN: 0214-1493

## Access Full Article

top## Abstract

top## How to cite

topMiret 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 -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.