Irregular Diophantine \(m\)-tuples and elliptic curves of high rank
type: Item
instance of: scholarly article
title: Irregular Diophantine \(m\)-tuples and elliptic curves of high rank
zbMATH Open document ID: 0964.11027
author: Andrej Dujella
published in: Proceedings of the Japan Academy. Series A
publication date: 2001-07-19T00:00:00Z
review text: A set of \(m\) non-zero rational numbers \(\{a_1,\ldots,a_m\}\) is called a \textit{Diophantine \(m\)-tuple} if for all \(1\leq i<j\leq m\) the rational number \(a_ia_j+1\) is a perfect square. In this very short note the author interprets certain properties of Diophantine \(4\)-tuples and \(5\)-tuples in terms of the existence of some relations connecting rational points of elliptic curves defined over \({\mathbb Q}\). As an application some elliptic curves over \({\mathbb Q}\) are found, whose Mordell-Weil group has rank \(8\) and torsion \(({\mathbb Z}/2{\mathbb Z})^2\).
reviewed by: Federico Pellarin
Mathematics Subject Classification ID: 11G05
Mathematics Subject Classification ID: 11B99
Mathematics Subject Classification ID: 14H52
zbMATH DE Number: 1538524
zbMATH Keywords: elliptic curves over the rational field
zbMATH Keywords: Diophantine \(m\)-tuple
zbMATH Keywords: high rank
zbMATH Keywords: rational points
zbMATH Keywords: Mordell-Weil group
describes a project that uses: ecdata
MaRDI profile type: Publication
full work available at URL: pjaa.76.66
OpenAlex ID: W2072443811
cites work: Q3208737
cites work: Q4341641
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cites work: Courbes elliptiques de rang ≥ 5 sur Q(t) avec un groupe de torsion isomorphe à Z/2Z × Z/2Z
DOI: 10.3792/PJAA.76.66
description: scientific article; zbMATH DE number 1538524