Volcanoes of \(\ell\)-isogenies of elliptic curves over finite fields: the case \(\ell=3^*\)
type: Item
instance of: scholarly article
title: Volcanoes of \(\ell\)-isogenies of elliptic curves over finite fields: the case \(\ell=3^*\)
zbMATH Open document ID: 1166.14023
DOI: 10.5565/PUBLMAT_PJTN05_08
author: R. Tomàs
author: Josep M. Miret Biosca
author: Daniel Sadornil
author: Juan Tena Ayuso
author: Magda Valls
published in: Publicacions Matemàtiques
publication date: 2009-06-05T00:00:00Z
full work available at URL: FileName:APJTN05 08.pdf
review text: From the abstract: This paper is devoted to the study of the volcanoes of \(\ell\)-isogenies of elliptic curves over 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 \(\ell\)-Sylow subgroup of an elliptic curve and the level of the volcano where it is placed. The particular case \(\ell=3\) is studied in detail, giving an algorithm to determine the volcano of \(3\)-isogenies of a given elliptic curve. Experimental results are also provided.
reviewed by: Christophe Ritzenthaler
Mathematics Subject Classification ID: 11G20
Mathematics Subject Classification ID: 14G15
Mathematics Subject Classification ID: 14K02
zbMATH DE Number: 5562419
zbMATH Keywords: elliptic curves
zbMATH Keywords: finite fields
zbMATH Keywords: isogenies
zbMATH Keywords: volcanoes
zbMATH Keywords: Sylow subgroup
zbMATH Keywords: algorithms
MaRDI profile type: Publication
OpenAlex ID: W2623202464
description: scientific article; zbMATH DE number 5562419