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

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 t...

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Detalhes bibliográficos
Autores: Miret, Josep M. (Josep Maria), Sadornil Renedo, Daniel, Tena Ayuso, Juan, Tomàs Cuñat, Rosa Ana, Valls Marsal, Magda
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2007
País:España
Recursos:Universitat de Lleida (UdL)
Repositorio:Repositori Obert UdL
OAI Identifier:oai:repositori.udl.cat:10459.1/44520
Acesso em linha:https://doi.org/10.5565/PUBLMAT_PJTN05_08
http://hdl.handle.net/10459.1/44520
Access Level:acceso abierto
Palavra-chave:Elliptic curves
Finite fields
Isogenies
Volcanoes
Corbes el·líptiques
Grups finits
Nombres, Teoria algebraica de
Descrição
Resumo: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.