{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,11]],"date-time":"2023-10-11T02:57:57Z","timestamp":1696993077019},"reference-count":29,"publisher":"Wiley","issue":"A","license":[{"start":{"date-parts":[[2014,8,1]],"date-time":"2014-08-01T00:00:00Z","timestamp":1406851200000},"content-version":"unspecified","delay-in-days":212,"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>In this paper we give a new formula for adding<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S1461157014000217_inline2\" \/><jats:tex-math>$2$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>-coverings and<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S1461157014000217_inline3\" \/><jats:tex-math>$3$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>-coverings of elliptic curves that avoids the need for any field extensions. We show that the<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S1461157014000217_inline4\" \/><jats:tex-math>$6$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>-coverings obtained can be represented by pairs of cubic forms. We then prove a theorem on the existence of such models with integer coefficients and the same discriminant as a minimal model for the Jacobian elliptic curve. This work has applications to finding rational points of large height on elliptic curves.<\/jats:p>","DOI":"10.1112\/s1461157014000217","type":"journal-article","created":{"date-parts":[[2014,8,5]],"date-time":"2014-08-05T10:34:15Z","timestamp":1407234855000},"page":"112-127","source":"Crossref","is-referenced-by-count":1,"title":["Minimal models for -coverings of elliptic curves"],"prefix":"10.1112","volume":"17","author":[{"given":"Tom","family":"Fisher","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2014,8,1]]},"reference":[{"key":"S1461157014000217_r26","volume-title":"A treatise on the higher plane curves","author":"Salmon","year":"1879"},{"key":"S1461157014000217_r25","volume-title":"The geometry of determinantal loci","author":"Room","year":"1938"},{"key":"S1461157014000217_r23","first-page":"29","volume-title":"Questions on Algebraic Varieties (C.I.M.E., III Ciclo, Varenna, 1969)","author":"Mumford","year":"1970"},{"key":"S1461157014000217_r22","article-title":"Projective geometry of elliptic curves","volume":"137","author":"Hulek","year":"1986","journal-title":"Ast\u00e9risque"},{"key":"S1461157014000217_r18","first-page":"317","volume-title":"Frontiers of mathematical sciences","author":"Gross","year":"2011"},{"key":"S1461157014000217_r17","doi-asserted-by":"publisher","DOI":"10.2140\/ant.2013.7.1179"},{"key":"S1461157014000217_r14","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2008.04.007"},{"key":"S1461157014000217_r15","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/pdn021"},{"key":"S1461157014000217_r11","doi-asserted-by":"publisher","DOI":"10.1016\/j.jnt.2004.10.001"},{"key":"S1461157014000217_r12","first-page":"121","article-title":"Explicit n-descent on elliptic curves, I. 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