{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,23]],"date-time":"2026-04-23T08:18:16Z","timestamp":1776932296881,"version":"3.51.2"},"reference-count":14,"publisher":"Wiley","license":[{"start":{"date-parts":[[2010,8,1]],"date-time":"2010-08-01T00:00:00Z","timestamp":1280620800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["LMS J. Comput. Math."],"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We discuss the Mordell\u2013Weil sieve as a general technique for proving results concerning rational points on a given curve. In the special case of curves of genus\u00a02, we describe quite explicitly how the relevant local information can be obtained if one does not want to restrict to mod\u00a0<jats:italic>p<\/jats:italic> information at primes of good reduction. We describe our implementation of the Mordell\u2013Weil sieve algorithm and discuss its efficiency.<\/jats:p><jats:p><jats:uri xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:type=\"simple\" xlink:href=\"http:\/\/journals.cambridge.org\/sup_S1461157009000187sup001\">Supplementary materials are available with this article.<\/jats:uri><\/jats:p>","DOI":"10.1112\/s1461157009000187","type":"journal-article","created":{"date-parts":[[2010,8,27]],"date-time":"2010-08-27T12:42:25Z","timestamp":1282912945000},"page":"272-306","source":"Crossref","is-referenced-by-count":55,"title":["The Mordell\u2013Weil sieve: proving non-existence of rational points on curves"],"prefix":"10.1112","volume":"13","author":[{"given":"Nils","family":"Bruin","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michael","family":"Stoll","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2010,8,1]]},"reference":[{"key":"S1461157009000187_ref30","first-page":"1967","volume":"4","author":"Stoll","year":"2007","journal-title":"Oberwolfach Rep."},{"key":"S1461157009000187_ref25","doi-asserted-by":"crossref","first-page":"183","DOI":"10.4064\/aa-90-2-183-201","volume":"90","author":"Stoll","year":"1999","journal-title":"Acta Arith."},{"key":"S1461157009000187_ref24","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-57878-6","volume-title":"Algebraic geometry I","author":"Shafarevich (ed.)","year":"1994"},{"key":"S1461157009000187_ref9","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1090\/S0025-5718-1987-0866101-0","volume":"48","author":"Cantor","year":"1987","journal-title":"Math. 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