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dc.contributor.authorvan Beek, Moniqueen
dc.contributor.authorFisher, Tomen
dc.date.accessioned2018-11-30T00:31:41Z
dc.date.available2018-11-30T00:31:41Z
dc.date.issued2018en
dc.identifier.issn0065-1036
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/286124
dc.description.abstractWe explain a method for computing the Cassels-Tate pairing on the 3-isogeny Selmer groups of an elliptic curve. This improves the upper bound on the rank of the elliptic curve coming from a descent by 3-isogeny, to that coming from a full 3-descent. One ingredient of our work is a new algorithm for solving cubic norm equations, that avoids the need for any S-unit computations. As an application, we show that the elliptic curves with torsion subgroup of order 3 and rank at least 13, found by Eroshkin, have rank exactly 13.
dc.publisherPolska Akademia Nauk
dc.subjectelliptic curvesen
dc.subjectCassels-Tate pairingen
dc.subjectdescenten
dc.subjectnorm equationsen
dc.titleComputing the Cassels-Tate pairing on 3-isogeny Selmer groups via cubic norm equationsen
dc.typeArticle
prism.endingPage396
prism.issueIdentifier4en
prism.publicationDate2018en
prism.publicationNameACTA ARITHMETICAen
prism.startingPage367
prism.volume185en
dc.identifier.doi10.17863/CAM.33439
dcterms.dateAccepted2018-04-09en
rioxxterms.versionofrecord10.4064/aa171108-11-4en
rioxxterms.licenseref.urihttp://www.rioxx.net/licenses/all-rights-reserveden
rioxxterms.licenseref.startdate2018en
dc.identifier.eissn1730-6264
rioxxterms.typeJournal Article/Reviewen
rioxxterms.freetoread.startdate2019-12-25


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