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On elliptic curves induced by rational diophantine quadruples

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dc.contributor.authorDujella, Andrej
dc.contributor.buuauthorSoydan, Gökhan
dc.contributor.buuauthorSOYDAN, GÖKHAN
dc.contributor.departmentBursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Anabilim Dalı.
dc.contributor.orcid0000-0001-6867-5811
dc.contributor.researcheridM-9459-2017
dc.date.accessioned2024-11-04T13:10:39Z
dc.date.available2024-11-04T13:10:39Z
dc.date.issued2022-01-01
dc.description.abstractIn this paper, we consider elliptic curves induced by rational Diophantine quadruples, i.e. sets of four non-zero rationals such that the product of any two of them plus 1 is a perfect square. We show that for each of the groups Z/2Z x Z/kZ for k = 2, 4, 6, 8, there are infinitely many rational Diophantine quadruples with the property that the induced elliptic curve has this torsion group. We also construct curves with moderately large rank in each of these four cases.
dc.description.sponsorshipCroatian Science Foundation IP-2018-01-1313
dc.description.sponsorshipQuantiXLie Center of Excellence - Croatian Government
dc.description.sponsorshipEuropean Union through the European Regional Development Fund -the Competitiveness and Cohesion Operational Programme KK.01.1.1.01. 0004
dc.description.sponsorshipResearch Fund of Bursa Uludag. University F2020/8
dc.description.sponsorshipCroatian Science Foundation IP-2018-01-1313
dc.description.sponsorshipQuantiXLie Center of Excellence - Croatian Government
dc.description.sponsorshipEuropean Union through the European Regional Development Fund -the Competitiveness and Cohesion Operational Programme KK.01.1.1.01. 0004
dc.identifier.doi10.3792/pjaa.98.001
dc.identifier.endpage6
dc.identifier.issn0386-2194
dc.identifier.issue1
dc.identifier.startpage1
dc.identifier.urihttps://doi.org/10.3792/pjaa.98.001
dc.identifier.urihttps://hdl.handle.net/11452/47411
dc.identifier.volume98
dc.identifier.wos000878614400001
dc.indexed.wosWOS.SCI
dc.language.isoen
dc.publisherJapan Acad
dc.relation.bapF2020/8
dc.relation.journalProceedings Of The Japan Academy Series A-mathematical Sciences
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.subjectRank
dc.subjectConstruction
dc.subjectSextuples
dc.subjectTriples
dc.subjectQ(t)
dc.subjectDiophantine quadruples
dc.subjectElliptic curves
dc.subjectTorsion group
dc.subjectRank
dc.subjectScience & technology
dc.subjectPhysical sciences
dc.subjectMathematics
dc.titleOn elliptic curves induced by rational diophantine quadruples
dc.typeArticle
dspace.entity.typePublication
relation.isAuthorOfPublication356f7af9-3f0f-4c82-8733-d98627634647
relation.isAuthorOfPublication.latestForDiscovery356f7af9-3f0f-4c82-8733-d98627634647

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