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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, 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 ; publishedVersion
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 original: https://www.raco.cat/index.php/PublicacionsMatematiques/article/view/10.5565-PUBLMAT_PJTN05_08
Adreça alternativa: https://www.raco.cat/index.php/PublicacionsMatematiques/article/view/69987
DOI: 10.5565/PUBLMAT_PJTN05_08


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Articles > Research articles

 Record created 2015-09-30, last modified 2019-04-17



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