A generalization of a result of Hurwitz and Mordell on the torsion subgroups of certain elliptic curves
type: Item
instance of: scholarly article
title: A generalization of a result of Hurwitz and Mordell on the torsion subgroups of certain elliptic curves
zbMATH Open document ID: 0756.14022
author: Chris K. Caldwell
published in: Rocky Mountain Journal of Mathematics
publication date: 1992-09-27T00:00:00Z
review text: Let \(k\) be an algebraic number field and let \(a,b,c,d\) be elements of \(k\) such that \(abc(d^ 3-27abc)\neq 0\). The author considers the elliptic curve given by \(E:aX^ 3+bY^ 3+cZ^ 3=dXYZ\) or rather the torsion subgroup of the group \(E(k)\) of points with coordinates in \(k\) (assuming such points exist). In case \(k=\mathbb{Q}\) there are classical results of Hurwitz and of Mordell. The author defines a certain map, resembling a height function, from \(E(k)\) into the set of integrals ideals of \(k\), which enables him to count the number of torsion points on the curve. Rather general results are obtained.
reviewed by: Roelof J. Stroeker
Mathematics Subject Classification ID: 14H52
Mathematics Subject Classification ID: 11G05
Mathematics Subject Classification ID: 14G05
Mathematics Subject Classification ID: 14G25
zbMATH DE Number: 61919
zbMATH Keywords: elliptic curve
zbMATH Keywords: height function
zbMATH Keywords: number of torsion points
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/rmjm/1181072796
OpenAlex ID: W1981537256
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DOI: 10.1216/RMJM/1181072796
description: scientific article; zbMATH DE number 61919