On elliptic curves induced by rational diophantine quadruples

Dujella, Andrej

Publication:
On elliptic curves induced by rational diophantine quadruples

dc.contributor.author	Dujella, Andrej
dc.contributor.buuauthor	Soydan, Gökhan
dc.contributor.buuauthor	SOYDAN, GÖKHAN
dc.contributor.department	Fen Edebiyat Fakültesi
dc.contributor.department	Matematik Ana Bilim Dalı
dc.contributor.orcid	0000-0001-6867-5811
dc.contributor.researcherid	M-9459-2017
dc.date.accessioned	2024-11-04T13:10:39Z
dc.date.available	2024-11-04T13:10:39Z
dc.date.issued	2022-01-01
dc.description.abstract	In 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.sponsorship	Croatian Science Foundation IP-2018-01-1313
dc.description.sponsorship	QuantiXLie Center of Excellence - Croatian Government
dc.description.sponsorship	European Union through the European Regional Development Fund -the Competitiveness and Cohesion Operational Programme KK.01.1.1.01. 0004
dc.description.sponsorship	Research Fund of Bursa Uludag. University F2020/8
dc.description.sponsorship	Croatian Science Foundation IP-2018-01-1313
dc.description.sponsorship	QuantiXLie Center of Excellence - Croatian Government
dc.description.sponsorship	European Union through the European Regional Development Fund -the Competitiveness and Cohesion Operational Programme KK.01.1.1.01. 0004
dc.identifier.doi	10.3792/pjaa.98.001
dc.identifier.endpage	6
dc.identifier.issn	0386-2194
dc.identifier.issue	1
dc.identifier.startpage	1
dc.identifier.uri	https://doi.org/10.3792/pjaa.98.001
dc.identifier.uri	https://hdl.handle.net/11452/47411
dc.identifier.volume	98
dc.identifier.wos	000878614400001
dc.indexed.wos	WOS.SCI
dc.language.iso	en
dc.publisher	Japan Acad
dc.relation.bap	F2020/8
dc.relation.journal	Proceedings Of The Japan Academy Series A-mathematical Sciences
dc.relation.publicationcategory	Makale - Uluslararası Hakemli Dergi
dc.rights	info:eu-repo/semantics/closedAccess
dc.subject	Rank
dc.subject	Construction
dc.subject	Sextuples
dc.subject	Triples
dc.subject	Q(t)
dc.subject	Diophantine quadruples
dc.subject	Elliptic curves
dc.subject	Torsion group
dc.subject	Rank
dc.subject	Science & technology
dc.subject	Physical sciences
dc.subject	Mathematics
dc.title	On elliptic curves induced by rational diophantine quadruples
dc.type	Article
dspace.entity.type	Publication
local.contributor.department	Fen Edebiyat Fakültesi/Matematik Ana Bilim Dalı
relation.isAuthorOfPublication	356f7af9-3f0f-4c82-8733-d98627634647
relation.isAuthorOfPublication.latestForDiscovery	356f7af9-3f0f-4c82-8733-d98627634647