Volcanoes of ℓ-isogenies of elliptic curves over finite fields : the case ℓ = 3
Miret, Josep M. (Universitat de Lleida. Departament de Matemàtica)
Sadornil, Daniel (Universidad de Salamanca. Departamento de Matemáticas)
Tena, Juan (Universidad de Valladolid. Departamento de Algebra, Análisis Matemático, Geometría y Topología)
Tomàs, Rosana (Universitat de Lleida. Departament de Matemàtica)
Valls, Magda (Universitat de Lleida. Departament de Matemàtica)

Date:	2007
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 also provided.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Elliptic curves ; Finite fields ; Isogenies ; Volcanoes ; ℓ-Sylow subgroup ; Algorithms
Published in:	Publicacions matemàtiques, Vol. Extra (2007) , p. 165-180, ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/69987
DOI: 10.5565/PUBLMAT_PJTN05_08

16 p, 196.4 KB

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