A simple proof of a theorem of Parish
type: Item
instance of: scholarly article
title: A simple proof of a theorem of Parish
zbMATH Open document ID: 0971.11031
author: Soonhak Kwon
published in: Proceedings of the Japan Academy. Series A
publication date: 2001-10-30T00:00:00Z
review text: The aim of this short note is to give a new proof of a result of \textit{J. L. Parish} [J. Number Theory 33, 257-265 (1989; Zbl 0703.14023)] that, in an elliptic curve \(E\) defined over a number field \(K\) with complex multiplication over \(\bar{K}\), a torsion point which is rational over \(K(j(E))\) has order \(1,2,3,4,6\) (here \(j(E)\) is the \(j\)-invariant of \(E\)). The proof uses elementary class field theory.
reviewed by: Federico Pellarin
Mathematics Subject Classification ID: 11G05
Mathematics Subject Classification ID: 14H52
Mathematics Subject Classification ID: 11G15
Mathematics Subject Classification ID: 14K22
zbMATH DE Number: 1443392
zbMATH Keywords: Fermat's curves
zbMATH Keywords: Jacobians
zbMATH Keywords: Mordell-Weil group
MaRDI profile type: Publication
full work available at URL: pjaa.75.170
OpenAlex ID: W2038036409
cites work: Q3996190
cites work: Arithmetic on elliptic curves with complex multiplication. With an appendix by B. Mazur
cites work: Q4855212
cites work: Rational torsion in complex-multiplication elliptic curves
cites work: Q4317891
DOI: 10.3792/PJAA.75.170
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description: scientific article; zbMATH DE number 1443392