{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T07:28:04Z","timestamp":1776842884387,"version":"3.51.2"},"reference-count":13,"publisher":"American Mathematical Society (AMS)","issue":"249","license":[{"start":{"date-parts":[[2005,3,4]],"date-time":"2005-03-04T00:00:00Z","timestamp":1109894400000},"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":"<p>\n                    In this paper we describe an algorithm that outputs the order and the structure, including generators, of the\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"2\">\n                        <mml:semantics>\n                          <mml:mn>2<\/mml:mn>\n                          <mml:annotation encoding=\"application\/x-tex\">2<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -Sylow subgroup of an elliptic curve over a finite field. To do this, we do not assume any knowledge of the group order. The results that lead to the design of this algorithm are of inductive type. Then a right choice of points allows us to reach the end within a linear number of successive halvings. The algorithm works with abscissas, so that halving of rational points in the elliptic curve becomes computing of square roots in the finite field. Efficient methods for this computation determine the efficiency of our algorithm.\n                  <\/p>","DOI":"10.1090\/s0025-5718-04-01640-0","type":"journal-article","created":{"date-parts":[[2004,9,20]],"date-time":"2004-09-20T09:57:53Z","timestamp":1095674273000},"page":"411-427","source":"Crossref","is-referenced-by-count":16,"title":["Determining the 2-Sylow subgroup of an elliptic curve over a finite field"],"prefix":"10.1090","volume":"74","author":[{"given":"J.","family":"Miret","sequence":"first","affiliation":[]},{"given":"R.","family":"Moreno","sequence":"additional","affiliation":[]},{"given":"A.","family":"Rio","sequence":"additional","affiliation":[]},{"given":"M.","family":"Valls","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2004,3,4]]},"reference":[{"key":"1","series-title":"Foundations of Computing Series","isbn-type":"print","volume-title":"Algorithmic number theory. 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Exemples et applications","author":"Mestre, J.-F.","year":"1986"},{"issue":"9","key":"9","first-page":"931","article-title":"Isomorphism classes of elliptic curves with even order over a finite field","volume":"2","author":"Miret, J.","year":"2002","journal-title":"Int. Math. J.","ISSN":"https:\/\/id.crossref.org\/issn\/1311-6797","issn-type":"print"},{"issue":"179","key":"10","doi-asserted-by":"publisher","first-page":"301","DOI":"10.2307\/2008268","article-title":"A note on elliptic curves over finite fields","volume":"49","author":"R\u00fcck, Hans-Georg","year":"1987","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"2","key":"11","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":"12","series-title":"Graduate Texts in Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-1920-8","volume-title":"The arithmetic of elliptic curves","volume":"106","author":"Silverman, Joseph H.","year":"1986","ISBN":"https:\/\/id.crossref.org\/isbn\/0387962034"},{"issue":"4","key":"13","doi-asserted-by":"crossref","first-page":"455","DOI":"10.24033\/bsmf.2107","article-title":"A note on elliptic curves over finite fields","volume":"116","author":"Voloch, J. F.","year":"1988","journal-title":"Bull. Soc. Math. 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