{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T18:47:31Z","timestamp":1776797251858,"version":"3.51.2"},"reference-count":8,"publisher":"American Mathematical Society (AMS)","issue":"290","license":[{"start":{"date-parts":[[2015,5,9]],"date-time":"2015-05-09T00:00:00Z","timestamp":1431129600000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"

\n In this paper, we describe a relation between the embedding degree of an elliptic curve over a prime field\n \n \n \n \n \n F<\/mml:mi>\n <\/mml:mrow>\n p<\/mml:mi>\n <\/mml:msub>\n \\mathbb {F}_p<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n and the inertial degree of the primes above\n \n \n \n p<\/mml:mi>\n p<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n in a certain ring class field. From this relation, we conclude that the embedding degree divides the class number of a group of binary quadratic forms of a fixed discriminant.\n <\/p>","DOI":"10.1090\/s0025-5718-2014-02831-7","type":"journal-article","created":{"date-parts":[[2014,5,9]],"date-time":"2014-05-09T13:56:38Z","timestamp":1399643798000},"page":"3001-3004","source":"Crossref","is-referenced-by-count":0,"title":["A relation between embedding degrees and class numbers of binary quadratic forms"],"prefix":"10.1090","volume":"83","author":[{"given":"San","family":"Ling","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Enver","family":"Ozdemir","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chaoping","family":"Xing","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2014,5,9]]},"reference":[{"issue":"2","key":"1","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1007\/s001459900040","article-title":"The improbability that an elliptic curve has subexponential discrete log problem under the Menezes-Okamoto-Vanstone algorithm","volume":"11","author":"Balasubramanian, R.","year":"1998","journal-title":"J. Cryptology","ISSN":"https:\/\/id.crossref.org\/issn\/0933-2790","issn-type":"print"},{"key":"2","isbn-type":"print","doi-asserted-by":"publisher","first-page":"213","DOI":"10.1007\/3-540-44647-8_13","article-title":"Identity-based encryption from the Weil pairing","author":"Boneh, Dan","year":"2001","ISBN":"https:\/\/id.crossref.org\/isbn\/3540424563"},{"key":"3","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4542-1","volume-title":"Binary quadratic forms","author":"Buell, Duncan A.","year":"1989","ISBN":"https:\/\/id.crossref.org\/isbn\/0387970371"},{"key":"4","series-title":"Discrete Mathematics and its Applications (Boca Raton)","isbn-type":"print","volume-title":"Handbook of elliptic and hyperelliptic curve cryptography","year":"2006","ISBN":"https:\/\/id.crossref.org\/isbn\/9781584885184"},{"key":"5","doi-asserted-by":"publisher","first-page":"197","DOI":"10.1007\/BF02940746","article-title":"Die Typen der Multiplikatorenringe elliptischer Funktionenk\u00f6rper","volume":"14","author":"Deuring, Max","year":"1941","journal-title":"Abh. Math. Sem. Hansischen Univ.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5858","issn-type":"print"},{"issue":"2","key":"6","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1016\/0097-3165(87)90003-3","article-title":"Nonsingular plane cubic curves over finite fields","volume":"46","author":"Schoof, Ren\u00e9","year":"1987","journal-title":"J. Combin. Theory Ser. A","ISSN":"https:\/\/id.crossref.org\/issn\/0097-3165","issn-type":"print"},{"key":"7","isbn-type":"print","first-page":"235","article-title":"Quadratic fields and factorization","author":"Schoof, R. J.","year":"1982","ISBN":"https:\/\/id.crossref.org\/isbn\/9061962498"},{"key":"8","series-title":"Discrete Mathematics and its Applications (Boca Raton)","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1201\/9781420071474","volume-title":"Elliptic curves","author":"Washington, Lawrence C.","year":"2008","ISBN":"https:\/\/id.crossref.org\/isbn\/9781420071467","edition":"2"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2014-83-290\/S0025-5718-2014-02831-7\/S0025-5718-2014-02831-7.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2014-83-290\/S0025-5718-2014-02831-7\/S0025-5718-2014-02831-7.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T18:08:03Z","timestamp":1776794883000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2014-83-290\/S0025-5718-2014-02831-7\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,5,9]]},"references-count":8,"journal-issue":{"issue":"290","published-print":{"date-parts":[[2014,11]]}},"alternative-id":["S0025-5718-2014-02831-7"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-2014-02831-7","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[2014,5,9]]}}}