{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T09:15:56Z","timestamp":1776849356028,"version":"3.51.2"},"reference-count":47,"publisher":"American Mathematical Society (AMS)","issue":"309","license":[{"start":{"date-parts":[[2018,5,5]],"date-time":"2018-05-05T00:00:00Z","timestamp":1525478400000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/501100006588","name":"Ministarstvo Znanosti, Obrazovanja i Sporta","doi-asserted-by":"publisher","award":["1115455"],"award-info":[{"award-number":["1115455"]}],"id":[{"id":"10.13039\/501100006588","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100006588","name":"Ministarstvo Znanosti, Obrazovanja i Sporta","doi-asserted-by":"publisher","award":["1522526"],"award-info":[{"award-number":["1522526"]}],"id":[{"id":"10.13039\/501100006588","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100008993","name":"Sveu?ili\u00c5\u00a1te u Zagrebu","doi-asserted-by":"publisher","award":["1115455"],"award-info":[{"award-number":["1115455"]}],"id":[{"id":"10.13039\/100008993","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100008993","name":"Sveu?ili\u00c5\u00a1te u Zagrebu","doi-asserted-by":"publisher","award":["1522526"],"award-info":[{"award-number":["1522526"]}],"id":[{"id":"10.13039\/100008993","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1115455"],"award-info":[{"award-number":["1115455"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1522526"],"award-info":[{"award-number":["1522526"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    Let\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper E slash double-struck upper Q\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>E<\/mml:mi>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mo>\/<\/mml:mo>\n                            <\/mml:mrow>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mi mathvariant=\"double-struck\">Q<\/mml:mi>\n                            <\/mml:mrow>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">E\/\\mathbb {Q}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    be an elliptic curve and let\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"double-struck upper Q left-parenthesis 3 Superscript normal infinity Baseline right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mi mathvariant=\"double-struck\">Q<\/mml:mi>\n                            <\/mml:mrow>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:msup>\n                              <mml:mn>3<\/mml:mn>\n                              <mml:mi mathvariant=\"normal\">\n                                \u221e\n                                \n                              <\/mml:mi>\n                            <\/mml:msup>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\mathbb {Q}(3^\\infty )<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    be the compositum of all cubic extensions of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"double-struck upper Q\">\n                        <mml:semantics>\n                          <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                            <mml:mi mathvariant=\"double-struck\">Q<\/mml:mi>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\mathbb {Q}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . In this article we show that the torsion subgroup of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper E left-parenthesis double-struck upper Q left-parenthesis 3 Superscript normal infinity Baseline right-parenthesis right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>E<\/mml:mi>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mi mathvariant=\"double-struck\">Q<\/mml:mi>\n                            <\/mml:mrow>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:msup>\n                              <mml:mn>3<\/mml:mn>\n                              <mml:mi mathvariant=\"normal\">\n                                \u221e\n                                \n                              <\/mml:mi>\n                            <\/mml:msup>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">E(\\mathbb {Q}(3^\\infty ))<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    is finite and we determine 20 possibilities for its structure, along with a complete description of the\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"double-struck upper Q overbar\">\n                        <mml:semantics>\n                          <mml:mover>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mi mathvariant=\"double-struck\">Q<\/mml:mi>\n                            <\/mml:mrow>\n                            <mml:mo accent=\"false\">\n                              \u00af\n                              \n                            <\/mml:mo>\n                          <\/mml:mover>\n                          <mml:annotation encoding=\"application\/x-tex\">\\overline {\\mathbb {Q}}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -isomorphism classes of elliptic curves that fall into each case. We provide rational parameterizations for each of the 16 torsion structures that occur for infinitely many\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"double-struck upper Q overbar\">\n                        <mml:semantics>\n                          <mml:mover>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mi mathvariant=\"double-struck\">Q<\/mml:mi>\n                            <\/mml:mrow>\n                            <mml:mo accent=\"false\">\n                              \u00af\n                              \n                            <\/mml:mo>\n                          <\/mml:mover>\n                          <mml:annotation encoding=\"application\/x-tex\">\\overline {\\mathbb {Q}}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -isomorphism classes of elliptic curves, and a complete list of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"j\">\n                        <mml:semantics>\n                          <mml:mi>j<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">j<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -invariants for each of the 4 that do not.\n                  <\/p>","DOI":"10.1090\/mcom\/3213","type":"journal-article","created":{"date-parts":[[2016,9,21]],"date-time":"2016-09-21T12:51:43Z","timestamp":1474462303000},"page":"425-458","source":"Crossref","is-referenced-by-count":14,"title":["Torsion subgroups of rational elliptic curves over the compositum of all cubic fields"],"prefix":"10.1090","volume":"87","author":[{"given":"Harris","family":"Daniels","sequence":"first","affiliation":[]},{"given":"\u00c1lvaro","family":"Lozano-Robledo","sequence":"additional","affiliation":[]},{"given":"Filip","family":"Najman","sequence":"additional","affiliation":[]},{"given":"Andrew","family":"Sutherland","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2017,5,5]]},"reference":[{"issue":"3-4","key":"1","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1006\/jsco.1996.0125","article-title":"The Magma algebra system. I. The user language","volume":"24","author":"Bosma, Wieb","year":"1997","journal-title":"J. Symbolic Comput.","ISSN":"https:\/\/id.crossref.org\/issn\/0747-7171","issn-type":"print"},{"key":"2","doi-asserted-by":"publisher","first-page":"603","DOI":"10.1016\/j.jnt.2015.09.013","article-title":"Torsion of rational elliptic curves over quartic Galois number fields","volume":"160","author":"Chou, Michael","year":"2016","journal-title":"J. Number Theory","ISSN":"https:\/\/id.crossref.org\/issn\/0022-314X","issn-type":"print"},{"key":"3","unstructured":"J. E. Cremona, Elliptic curve data, database available at http:\/\/homepages.warwick.ac.uk\/ ~masgaj\/ftp\/data\/."},{"issue":"2","key":"4","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1080\/10586458.2003.10504495","article-title":"Congruence subgroups of \ud835\udc43\ud835\udc46\ud835\udc3f(2,\u2124) of genus less than or equal to 24","volume":"12","author":"Cummins, C. J.","year":"2003","journal-title":"Experiment. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/1058-6458","issn-type":"print"},{"key":"5","unstructured":"H. Daniels, \u00c1. Lozano-Robledo, J. Morrow, F. Najman, and A.V. Sutherland, Magma scripts related to Torsion subgroups of rational elliptic curves over the compositum of all cubic fields, available at http:\/\/math.mit.edu\/ drew."},{"issue":"3","key":"6","doi-asserted-by":"publisher","first-page":"349","DOI":"10.1007\/BF01388432","article-title":"Endlichkeitss\u00e4tze f\u00fcr abelsche Variet\u00e4ten \u00fcber Zahlk\u00f6rpern","volume":"73","author":"Faltings, G.","year":"1983","journal-title":"Invent. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0020-9910","issn-type":"print"},{"key":"7","doi-asserted-by":"publisher","first-page":"112","DOI":"10.1112\/plms\/s3-28.1.112","article-title":"Approximation theory and the rank of abelian varieties over large algebraic fields","volume":"28","author":"Frey, Gerhard","year":"1974","journal-title":"Proc. London Math. Soc. (3)","ISSN":"https:\/\/id.crossref.org\/issn\/0024-6115","issn-type":"print"},{"issue":"1","key":"8","doi-asserted-by":"publisher","first-page":"29","DOI":"10.4064\/aa115-1-3","article-title":"Torsion subgroups of elliptic curves with non-cyclic torsion over \u211a in elementary abelian 2-extensions of \u211a","volume":"115","author":"Fujita, Yasutsugu","year":"2004","journal-title":"Acta Arith.","ISSN":"https:\/\/id.crossref.org\/issn\/0065-1036","issn-type":"print"},{"issue":"1","key":"9","doi-asserted-by":"publisher","first-page":"124","DOI":"10.1016\/j.jnt.2005.03.005","article-title":"Torsion subgroups of elliptic curves in elementary abelian 2-extensions of \u211a","volume":"114","author":"Fujita, Yasutsugu","year":"2005","journal-title":"J. Number Theory","ISSN":"https:\/\/id.crossref.org\/issn\/0022-314X","issn-type":"print"},{"issue":"3","key":"10","doi-asserted-by":"publisher","first-page":"655","DOI":"10.5802\/jtnb.884","article-title":"On the compositum of all degree \ud835\udc51 extensions of a number field","volume":"26","author":"Gal, Itamar","year":"2014","journal-title":"J. Th\\'{e}or. Nombres Bordeaux","ISSN":"https:\/\/id.crossref.org\/issn\/1246-7405","issn-type":"print"},{"key":"11","doi-asserted-by":"publisher","first-page":"409","DOI":"10.1007\/BF01187387","article-title":"Normalteiler und maximale Untergruppen endlicher Gruppen","volume":"60","author":"Huppert, Bertram","year":"1954","journal-title":"Math. Z.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5874","issn-type":"print"},{"issue":"273","key":"12","doi-asserted-by":"publisher","first-page":"579","DOI":"10.1090\/S0025-5718-10-02369-0","article-title":"Families of elliptic curves over cubic number fields with prescribed torsion subgroups","volume":"80","author":"Jeon, Daeyeol","year":"2011","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"276","key":"13","doi-asserted-by":"publisher","first-page":"2395","DOI":"10.1090\/S0025-5718-2011-02493-2","article-title":"Families of elliptic curves over quartic number fields with prescribed torsion subgroups","volume":"80","author":"Jeon, Daeyeol","year":"2011","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"1","key":"14","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1112\/S0024610706022940","article-title":"On the torsion of elliptic curves over quartic number fields","volume":"74","author":"Jeon, Daeyeol","year":"2006","journal-title":"J. London Math. Soc. (2)","ISSN":"https:\/\/id.crossref.org\/issn\/0024-6107","issn-type":"print"},{"issue":"3","key":"15","doi-asserted-by":"publisher","first-page":"291","DOI":"10.4064\/aa113-3-6","article-title":"On the torsion of elliptic curves over cubic number fields","volume":"113","author":"Jeon, Daeyeol","year":"2004","journal-title":"Acta Arith.","ISSN":"https:\/\/id.crossref.org\/issn\/0065-1036","issn-type":"print"},{"issue":"2","key":"16","doi-asserted-by":"publisher","first-page":"221","DOI":"10.1007\/BF01232025","article-title":"Torsion points on elliptic curves and \ud835\udc5e-coefficients of modular forms","volume":"109","author":"Kamienny, S.","year":"1992","journal-title":"Invent. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0020-9910","issn-type":"print"},{"issue":"2","key":"17","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1016\/0022-314X(82)90025-7","article-title":"On the number of \ud835\udc44-isomorphism classes of elliptic curves in each \ud835\udc44-isogeny class","volume":"15","author":"Kenku, M. A.","year":"1982","journal-title":"J. Number Theory","ISSN":"https:\/\/id.crossref.org\/issn\/0022-314X","issn-type":"print"},{"issue":"1","key":"18","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1017\/S0305004100055444","article-title":"The modular curve \ud835\udc4b\u2080(39) and rational isogeny","volume":"85","author":"Kenku, M. A.","year":"1979","journal-title":"Math. Proc. Cambridge Philos. Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0305-0041","issn-type":"print"},{"issue":"1","key":"19","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1017\/S0305004100056462","article-title":"The modular curves \ud835\udc4b\u2080(65) and \ud835\udc4b\u2080(91) and rational isogeny","volume":"87","author":"Kenku, M. A.","year":"1980","journal-title":"Math. Proc. Cambridge Philos. Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0305-0041","issn-type":"print"},{"issue":"2","key":"20","doi-asserted-by":"publisher","first-page":"239","DOI":"10.1112\/jlms\/s2-22.2.239","article-title":"The modular curve \ud835\udc4b\u2080(169) and rational isogeny","volume":"22","author":"Kenku, M. A.","year":"1980","journal-title":"J. London Math. Soc. (2)","ISSN":"https:\/\/id.crossref.org\/issn\/0024-6107","issn-type":"print"},{"issue":"3","key":"21","doi-asserted-by":"publisher","first-page":"415","DOI":"10.1112\/jlms\/s2-23.3.415","article-title":"On the modular curves \ud835\udc4b\u2080(125), \ud835\udc4b\u2081(25) and \ud835\udc4b\u2081(49)","volume":"23","author":"Kenku, M. A.","year":"1981","journal-title":"J. London Math. Soc. (2)","ISSN":"https:\/\/id.crossref.org\/issn\/0024-6107","issn-type":"print"},{"key":"22","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1017\/S0027763000002816","article-title":"Torsion points on elliptic curves defined over quadratic fields","volume":"109","author":"Kenku, M. A.","year":"1988","journal-title":"Nagoya Math. J.","ISSN":"https:\/\/id.crossref.org\/issn\/0027-7630","issn-type":"print"},{"key":"23","doi-asserted-by":"publisher","first-page":"163","DOI":"10.1515\/crll.1985.355.163","article-title":"Rational points on elliptic curves over \ud835\udc44 in elementary abelian 2-extensions of \ud835\udc44","volume":"355","author":"Laska, Michael","year":"1985","journal-title":"J. Reine Angew. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0075-4102","issn-type":"print"},{"key":"24","unstructured":"LMFDB Collaboration, The L-functions and modular forms database, available at http:\/\/www.lmfdb.org."},{"issue":"1","key":"25","doi-asserted-by":"publisher","first-page":"279","DOI":"10.1007\/s00208-013-0906-5","article-title":"On the field of definition of \ud835\udc5d-torsion points on elliptic curves over the rationals","volume":"357","author":"Lozano-Robledo, \u00c1lvaro","year":"2013","journal-title":"Math. Ann.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5831","issn-type":"print"},{"issue":"4","key":"26","doi-asserted-by":"publisher","first-page":"1311","DOI":"10.4171\/RMI\/870","article-title":"Division fields of elliptic curves with minimal ramification","volume":"31","author":"Lozano-Robledo, \u00c1lvaro","year":"2015","journal-title":"Rev. Mat. Iberoam.","ISSN":"https:\/\/id.crossref.org\/issn\/0213-2230","issn-type":"print"},{"key":"27","unstructured":"\u00c1. Lozano-Robledo, Uniform boundedness in terms of ramification, preprint, available at http:\/\/alozano.clas.uconn.edu\/research-articles\/."},{"issue":"47","key":"28","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1007\/BF02684339","article-title":"Modular curves and the Eisenstein ideal","author":"Mazur, B.","year":"1977","journal-title":"Inst. Hautes \\'{E}tudes Sci. Publ. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0073-8301","issn-type":"print"},{"issue":"2","key":"29","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1007\/BF01390348","article-title":"Rational isogenies of prime degree (with an appendix by D. Goldfeld)","volume":"44","author":"Mazur, B.","year":"1978","journal-title":"Invent. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0020-9910","issn-type":"print"},{"issue":"208","key":"30","doi-asserted-by":"publisher","first-page":"767","DOI":"10.2307\/2153297","article-title":"Computing division polynomials","volume":"63","author":"McKee, James","year":"1994","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"1-3","key":"31","doi-asserted-by":"publisher","first-page":"437","DOI":"10.1007\/s002220050059","article-title":"Bornes pour la torsion des courbes elliptiques sur les corps de nombres","volume":"124","author":"Merel, Lo\u00efc","year":"1996","journal-title":"Invent. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0020-9910","issn-type":"print"},{"key":"32","unstructured":"L. J. Mordell, On the rational solutions of the indeterminate equations of the third and fourth degrees, Proc. Cambridge Philos. Soc. 21 (1922) 179\u2013192."},{"issue":"1","key":"33","doi-asserted-by":"publisher","first-page":"245","DOI":"10.4310\/MRL.2016.v23.n1.a12","article-title":"Torsion of rational elliptic curves over cubic fields and sporadic points on \ud835\udc4b\u2081(\ud835\udc5b)","volume":"23","author":"Najman, Filip","year":"2016","journal-title":"Math. Res. Lett.","ISSN":"https:\/\/id.crossref.org\/issn\/1073-2780","issn-type":"print"},{"key":"34","doi-asserted-by":"publisher","first-page":"85","DOI":"10.1515\/crll.1999.009","article-title":"Bornes effectives pour la torsion des courbes elliptiques sur les corps de nombres","volume":"506","author":"Parent, Pierre","year":"1999","journal-title":"J. Reine Angew. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0075-4102","issn-type":"print"},{"key":"35","unstructured":"H. Poincar\u00e9 Sur les propri\u00e9t\u00e9s arithm\u00e9tiques des courbes alg\u00e9briques, J. Math. Pures Appl. Ser 5. 7 (1901), 161\u2013233."},{"issue":"3-4","key":"36","first-page":"285","article-title":"Finiteness theorems in geometric classfield theory","volume":"27","author":"Katz, Nicholas M.","year":"1981","journal-title":"Enseign. Math. (2)","ISSN":"https:\/\/id.crossref.org\/issn\/0013-8584","issn-type":"print"},{"key":"37","series-title":"Graduate Texts in Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-8594-1","volume-title":"A course in the theory of groups","volume":"80","author":"Robinson, Derek J. S.","year":"1996","ISBN":"https:\/\/id.crossref.org\/isbn\/0387944613","edition":"2"},{"key":"38","doi-asserted-by":"publisher","first-page":"Paper No. 12, 34","DOI":"10.1007\/s40993-015-0013-7","article-title":"Elliptic curves over \u211a and 2-adic images of Galois","volume":"1","author":"Rouse, Jeremy","year":"2015","journal-title":"Res. Number Theory","ISSN":"https:\/\/id.crossref.org\/issn\/2522-0160","issn-type":"print"},{"issue":"4","key":"39","doi-asserted-by":"publisher","first-page":"259","DOI":"10.1007\/BF01405086","article-title":"Propri\u00e9t\u00e9s galoisiennes des points d\u2019ordre fini des courbes elliptiques","volume":"15","author":"Serre, Jean-Pierre","year":"1972","journal-title":"Invent. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0020-9910","issn-type":"print"},{"key":"40","series-title":"Graduate Texts in Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-09494-6","volume-title":"The arithmetic of elliptic curves","volume":"106","author":"Silverman, Joseph H.","year":"2009","ISBN":"https:\/\/id.crossref.org\/isbn\/9780387094939","edition":"2"},{"issue":"2","key":"41","doi-asserted-by":"publisher","first-page":"475","DOI":"10.5802\/jtnb.807","article-title":"A local-global principle for rational isogenies of prime degree","volume":"24","author":"Sutherland, Andrew V.","year":"2012","journal-title":"J. Th\\'{e}or. Nombres Bordeaux","ISSN":"https:\/\/id.crossref.org\/issn\/1246-7405","issn-type":"print"},{"key":"42","doi-asserted-by":"publisher","first-page":"Paper No. e4, 79","DOI":"10.1017\/fms.2015.33","article-title":"Computing images of Galois representations attached to elliptic curves","volume":"4","author":"Sutherland, Andrew V.","year":"2016","journal-title":"Forum Math. Sigma"},{"key":"43","unstructured":"A.V. Sutherland and D. Zywina, Modular curves of prime power level with infinitely many rational points, to appear in Algebra and Number Theory, available at https:\/\/arxiv.org\/abs\/1605.03988."},{"issue":"1","key":"44","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1007\/BF02547409","article-title":"L\u2019arithm\u00e9tique sur les courbes alg\u00e9briques","volume":"52","author":"Weil, Andr\u00e9","year":"1929","journal-title":"Acta Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0001-5962","issn-type":"print"},{"key":"45","first-page":"511","article-title":"Remark on a recent paper of O. Ore","volume":"6","author":"Zappa, Guido","year":"1940","journal-title":"Duke Math. J.","ISSN":"https:\/\/id.crossref.org\/issn\/0012-7094","issn-type":"print"},{"key":"46","unstructured":"D. Zywina, On the possible images of mod \u2113 representations associated to elliptic curves over \u211a, preprint, available at http:\/\/arxiv.org\/abs\/1508.07660."},{"key":"47","unstructured":"D. Zywina, Possible indices for the Galois image of elliptic curves over \u211a, preprint, available at http:\/\/arxiv.org\/abs\/1508.07663."}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.ams.org\/mcom\/2018-87-309\/S0025-5718-2017-03213-0\/mcom3213_AM.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"http:\/\/www.ams.org\/mcom\/2018-87-309\/S0025-5718-2017-03213-0\/S0025-5718-2017-03213-0.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2018-87-309\/S0025-5718-2017-03213-0\/S0025-5718-2017-03213-0.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T19:28:06Z","timestamp":1776799686000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2018-87-309\/S0025-5718-2017-03213-0\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,5,5]]},"references-count":47,"journal-issue":{"issue":"309","published-print":{"date-parts":[[2018,1]]}},"alternative-id":["S0025-5718-2017-03213-0"],"URL":"https:\/\/doi.org\/10.1090\/mcom\/3213","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":[[2017,5,5]]}}}