{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T12:38:34Z","timestamp":1773232714958,"version":"3.50.1"},"reference-count":19,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2014,6,1]],"date-time":"2014-06-01T00:00:00Z","timestamp":1401580800000},"content-version":"unspecified","delay-in-days":151,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["LMS J. Comput. Math."],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We construct an elliptic curve over the field of rational functions with torsion group<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S1461157014000023_inline2\"\/><jats:tex-math>$\\mathbb{Z}\/2\\mathbb{Z}\\times \\mathbb{Z}\/4\\mathbb{Z}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>and rank equal to four, and an elliptic curve over<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S1461157014000023_inline3\"\/><jats:tex-math>$\\mathbb{Q}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>with the same torsion group and rank nine. Both results improve previous records for ranks of curves of this torsion group. They are obtained by considering elliptic curves induced by Diophantine triples.<\/jats:p>","DOI":"10.1112\/s1461157014000023","type":"journal-article","created":{"date-parts":[[2014,6,11]],"date-time":"2014-06-11T04:02:44Z","timestamp":1402459364000},"page":"282-288","source":"Crossref","is-referenced-by-count":16,"title":["High-rank elliptic curves with torsion induced by Diophantine triples"],"prefix":"10.1112","volume":"17","author":[{"given":"Andrej","family":"Dujella","sequence":"first","affiliation":[]},{"given":"Juan Carlos","family":"Peral","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2014,6,1]]},"reference":[{"key":"S1461157014000023_r9","article-title":"Elliptic curves coming from Heron triangles","author":"Dujella","journal-title":"Rocky Mountain J. Math."},{"key":"S1461157014000023_r8","unstructured":"8. A. 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Tadi\u0107 , \u2018Injectivity of the specialization homomorphism of elliptic curves\u2019, Preprint, 2012, arXiv:1211.3851.","DOI":"10.3336\/gm.47.2.03"},{"key":"S1461157014000023_r16","first-page":"209","article-title":"Formules explicites et minorations de conducteurs de vari\u00e9t\u00e9s alg\u00e9briques","volume":"58","author":"Mestre","year":"1986","journal-title":"Compositio Math."},{"key":"S1461157014000023_r18","unstructured":"18. PARI\/GP, version 2.4.0, Bordeaux, 2008, http:\/\/pari.math.u-bordeaux.fr."},{"key":"S1461157014000023_r11","article-title":"Three lectures on elliptic surfaces and curves of high rank","author":"Elkies","year":"2007","journal-title":"Lecture notes, Oberwolfach"},{"key":"S1461157014000023_r2","unstructured":"2. G. Campbell and E. H. 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