{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T06:01:59Z","timestamp":1776837719403,"version":"3.51.2"},"reference-count":41,"publisher":"American Mathematical Society (AMS)","issue":"346","license":[{"start":{"date-parts":[[2024,8,30]],"date-time":"2024-08-30T00:00:00Z","timestamp":1724976000000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/100000893","name":"Simons Foundation","doi-asserted-by":"publisher","award":["550023"],"award-info":[{"award-number":["550023"]}],"id":[{"id":"10.13039\/100000893","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000893","name":"Simons Foundation","doi-asserted-by":"publisher","award":["Grant KK.01.1.1.01.0004"],"award-info":[{"award-number":["Grant KK.01.1.1.01.0004"]}],"id":[{"id":"10.13039\/100000893","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000893","name":"Simons Foundation","doi-asserted-by":"publisher","award":["DMS-1945452"],"award-info":[{"award-number":["DMS-1945452"]}],"id":[{"id":"10.13039\/100000893","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000893","name":"Simons Foundation","doi-asserted-by":"publisher","award":["550023"],"award-info":[{"award-number":["550023"]}],"id":[{"id":"10.13039\/100000893","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100008530","name":"European Regional Development Fund","doi-asserted-by":"publisher","award":["550023"],"award-info":[{"award-number":["550023"]}],"id":[{"id":"10.13039\/501100008530","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100008530","name":"European Regional Development Fund","doi-asserted-by":"publisher","award":["Grant KK.01.1.1.01.0004"],"award-info":[{"award-number":["Grant KK.01.1.1.01.0004"]}],"id":[{"id":"10.13039\/501100008530","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100008530","name":"European Regional Development Fund","doi-asserted-by":"publisher","award":["DMS-1945452"],"award-info":[{"award-number":["DMS-1945452"]}],"id":[{"id":"10.13039\/501100008530","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100008530","name":"European Regional Development Fund","doi-asserted-by":"publisher","award":["550023"],"award-info":[{"award-number":["550023"]}],"id":[{"id":"10.13039\/501100008530","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["550023"],"award-info":[{"award-number":["550023"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["Grant KK.01.1.1.01.0004"],"award-info":[{"award-number":["Grant KK.01.1.1.01.0004"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1945452"],"award-info":[{"award-number":["DMS-1945452"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["550023"],"award-info":[{"award-number":["550023"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000893","name":"Simons Foundation","doi-asserted-by":"publisher","award":["550023"],"award-info":[{"award-number":["550023"]}],"id":[{"id":"10.13039\/100000893","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000893","name":"Simons Foundation","doi-asserted-by":"publisher","award":["Grant KK.01.1.1.01.0004"],"award-info":[{"award-number":["Grant KK.01.1.1.01.0004"]}],"id":[{"id":"10.13039\/100000893","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000893","name":"Simons Foundation","doi-asserted-by":"publisher","award":["DMS-1945452"],"award-info":[{"award-number":["DMS-1945452"]}],"id":[{"id":"10.13039\/100000893","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000893","name":"Simons Foundation","doi-asserted-by":"publisher","award":["550023"],"award-info":[{"award-number":["550023"]}],"id":[{"id":"10.13039\/100000893","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    Building on Mazur\u2019s 1978 work on prime degree isogenies, Kenku determined in 1981 all possible cyclic isogenies of elliptic curves over\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                    . Although more than 40 years have passed, the determination of cyclic isogenies of elliptic curves over a single other number field has hitherto not been realised.\n                  <\/p>\n                  <p>\n                    In this paper we develop a procedure to assist in establishing such a determination for a given quadratic field. Executing this procedure on all quadratic fields\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 StartRoot d EndRoot 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:msqrt>\n                              <mml:mi>d<\/mml:mi>\n                            <\/mml:msqrt>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\mathbb {Q}(\\sqrt {d})<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    with\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"StartAbsoluteValue d EndAbsoluteValue greater-than 10 Superscript 4\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mo stretchy=\"false\">|<\/mml:mo>\n                            <\/mml:mrow>\n                            <mml:mi>d<\/mml:mi>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mo stretchy=\"false\">|<\/mml:mo>\n                            <\/mml:mrow>\n                            <mml:mo>&gt;<\/mml:mo>\n                            <mml:msup>\n                              <mml:mn>10<\/mml:mn>\n                              <mml:mn>4<\/mml:mn>\n                            <\/mml:msup>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">|d| &gt; 10^4<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    we obtain, conditional on the Generalised Riemann Hypothesis, the determination of cyclic isogenies of elliptic curves over\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"19\">\n                        <mml:semantics>\n                          <mml:mn>19<\/mml:mn>\n                          <mml:annotation encoding=\"application\/x-tex\">19<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    quadratic fields, including\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 StartRoot 213 EndRoot 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:msqrt>\n                              <mml:mn>213<\/mml:mn>\n                            <\/mml:msqrt>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\mathbb {Q}(\\sqrt {213})<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    and\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 StartRoot negative 2289 EndRoot 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:msqrt>\n                              <mml:mo>\n                                \u2212\n                                \n                              <\/mml:mo>\n                              <mml:mn>2289<\/mml:mn>\n                            <\/mml:msqrt>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\mathbb {Q}(\\sqrt {-2289})<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . To make this procedure work, we determine all of the finitely many quadratic points on the modular curves\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper X 0 left-parenthesis 125 right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msub>\n                              <mml:mi>X<\/mml:mi>\n                              <mml:mn>0<\/mml:mn>\n                            <\/mml:msub>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mn>125<\/mml:mn>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">X_0(125)<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    and\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper X 0 left-parenthesis 169 right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msub>\n                              <mml:mi>X<\/mml:mi>\n                              <mml:mn>0<\/mml:mn>\n                            <\/mml:msub>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mn>169<\/mml:mn>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">X_0(169)<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    , which may be of independent interest.\n                  <\/p>","DOI":"10.1090\/mcom\/3894","type":"journal-article","created":{"date-parts":[[2023,8,2]],"date-time":"2023-08-02T09:53:42Z","timestamp":1690970022000},"page":"841-862","source":"Crossref","is-referenced-by-count":8,"title":["Cyclic isogenies of elliptic curves over fixed quadratic fields"],"prefix":"10.1090","volume":"93","author":[{"given":"Barinder","family":"Banwait","sequence":"first","affiliation":[]},{"given":"Filip","family":"Najman","sequence":"additional","affiliation":[]},{"given":"Oana","family":"Padurariu","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2023,8,30]]},"reference":[{"issue":"1","key":"1","doi-asserted-by":"publisher","first-page":"15","DOI":"10.4064\/aa220110-7-3","article-title":"Quadratic Chabauty for Atkin-Lehner quotients of modular curves of prime level and genus 4, 5, 6","volume":"208","author":"Ad\u017eaga, Nikola","year":"2023","journal-title":"Acta Arith.","ISSN":"https:\/\/id.crossref.org\/issn\/0065-1036","issn-type":"print"},{"key":"2","unstructured":"[AM] V. Arul and J. Steffen M\u00fcller, Rational points on \ud835\udc4b\u2080\u207a(125), preprint, available at  arXiv:2205.14744, 2022."},{"issue":"14","key":"3","doi-asserted-by":"publisher","first-page":"11829","DOI":"10.1093\/imrn\/rnac134","article-title":"Explicit isogenies of prime degree over quadratic fields","author":"Banwait, Barinder S.","year":"2023","journal-title":"Int. Math. Res. Not. IMRN","ISSN":"https:\/\/id.crossref.org\/issn\/1073-7928","issn-type":"print"},{"issue":"3-4","key":"4","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"},{"issue":"14","key":"5","doi-asserted-by":"publisher","first-page":"11829","DOI":"10.1093\/imrn\/rnac134","article-title":"Explicit isogenies of prime degree over quadratic fields","author":"Banwait, Barinder S.","year":"2023","journal-title":"Int. Math. Res. Not. IMRN","ISSN":"https:\/\/id.crossref.org\/issn\/1073-7928","issn-type":"print"},{"issue":"3","key":"6","doi-asserted-by":"publisher","first-page":"885","DOI":"10.4007\/annals.2019.189.3.6","article-title":"Explicit Chabauty-Kim for the split Cartan modular curve of level 13","volume":"189","author":"Balakrishnan, Jennifer","year":"2019","journal-title":"Ann. of Math. (2)","ISSN":"https:\/\/id.crossref.org\/issn\/0003-486X","issn-type":"print"},{"issue":"7","key":"7","doi-asserted-by":"publisher","first-page":"5604","DOI":"10.1093\/imrn\/rnab358","article-title":"Cubic and quartic points on modular curves using generalised symmetric Chabauty","author":"Box, Josha","year":"2023","journal-title":"Int. Math. Res. Not. IMRN","ISSN":"https:\/\/id.crossref.org\/issn\/1073-7928","issn-type":"print"},{"issue":"4","key":"8","doi-asserted-by":"publisher","first-page":"1001","DOI":"10.1142\/S1793042111004538","article-title":"Crit\u00e8res d\u2019irr\u00e9ductibilit\u00e9 pour les repr\u00e9sentations des courbes elliptiques","volume":"7","author":"Billerey, Nicolas","year":"2011","journal-title":"Int. J. Number Theory","ISSN":"https:\/\/id.crossref.org\/issn\/1793-0421","issn-type":"print"},{"key":"9","doi-asserted-by":"publisher","first-page":"Paper No. 3, 13","DOI":"10.1007\/s40993-015-0031-5","article-title":"A criterion to rule out torsion groups for elliptic curves over number fields","volume":"2","author":"Bruin, Peter","year":"2016","journal-title":"Res. Number Theory","ISSN":"https:\/\/id.crossref.org\/issn\/2522-0160","issn-type":"print"},{"issue":"327","key":"10","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1090\/mcom\/3547","article-title":"Quadratic points on modular curves with infinite Mordell-Weil group","volume":"90","author":"Box, Josha","year":"2021","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":"825","DOI":"10.1112\/jlms.12518","article-title":"The least degree of a CM point on a modular curve","volume":"105","author":"Clark, Pete L.","year":"2022","journal-title":"J. Lond. Math. Soc. (2)","ISSN":"https:\/\/id.crossref.org\/issn\/0024-6107","issn-type":"print"},{"key":"12","isbn-type":"print","volume-title":"Algorithms for modular elliptic curves","author":"Cremona, J. E.","year":"1997","ISBN":"https:\/\/id.crossref.org\/isbn\/0521598206","edition":"2"},{"issue":"7","key":"13","doi-asserted-by":"publisher","first-page":"1837","DOI":"10.2140\/ant.2021.15.1837","article-title":"Sporadic cubic torsion","volume":"15","author":"Derickx, Maarten","year":"2021","journal-title":"Algebra Number Theory","ISSN":"https:\/\/id.crossref.org\/issn\/1937-0652","issn-type":"print"},{"issue":"2","key":"14","doi-asserted-by":"publisher","first-page":"267","DOI":"10.2140\/ant.2023.17.267","article-title":"Torsion points on elliptic curves over number fields of small degree","volume":"17","author":"Derickx, Maarten","year":"2023","journal-title":"Algebra Number Theory","ISSN":"https:\/\/id.crossref.org\/issn\/1937-0652","issn-type":"print"},{"issue":"2","key":"15","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1007\/BF01388809","article-title":"Heegner points and derivatives of \ud835\udc3f-series","volume":"84","author":"Gross, Benedict H.","year":"1986","journal-title":"Invent. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0020-9910","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":"1","key":"17","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":"2","key":"18","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":"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":"3","key":"20","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"},{"issue":"5","key":"21","first-page":"171","article-title":"Finiteness of the Shafarevich-Tate group and the group of rational points for some modular abelian varieties","volume":"1","author":"Kolyvagin, V. A.","year":"1989","journal-title":"Algebra i Analiz","ISSN":"https:\/\/id.crossref.org\/issn\/0234-0852","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","isbn-type":"print","first-page":"435","article-title":"Euler systems","author":"Kolyvagin, V. A.","year":"1990","ISBN":"https:\/\/id.crossref.org\/isbn\/0817634282"},{"issue":"3","key":"24","doi-asserted-by":"publisher","first-page":"747","DOI":"10.2140\/ant.2021.15.747","article-title":"Residual Galois representations of elliptic curves with image contained in the normaliser of a nonsplit Cartan","volume":"15","author":"Le Fourn, Samuel","year":"2021","journal-title":"Algebra Number Theory","ISSN":"https:\/\/id.crossref.org\/issn\/1937-0652","issn-type":"print"},{"issue":"3","key":"25","doi-asserted-by":"publisher","first-page":"517","DOI":"10.1017\/S1474748013000182","article-title":"Determinants of subquotients of Galois representations associated with abelian varieties","volume":"13","author":"Larson, Eric","year":"2014","journal-title":"J. Inst. Math. Jussieu","ISSN":"https:\/\/id.crossref.org\/issn\/1474-7480","issn-type":"print"},{"issue":"47","key":"26","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":"27","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":"1-3","key":"28","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"},{"issue":"4","key":"29","doi-asserted-by":"publisher","first-page":"319","DOI":"10.4064\/aa210812-2-4","article-title":"Fermat\u2019s last theorem and modular curves over real quadratic fields","volume":"203","author":"Michaud-Jacobs, Philippe","year":"2022","journal-title":"Acta Arith.","ISSN":"https:\/\/id.crossref.org\/issn\/0065-1036","issn-type":"print"},{"key":"30","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/BF01389997","article-title":"Arithmetic of Weil curves","volume":"25","author":"Mazur, B.","year":"1974","journal-title":"Invent. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0020-9910","issn-type":"print"},{"issue":"9","key":"31","doi-asserted-by":"publisher","first-page":"1964","DOI":"10.1016\/j.jnt.2009.12.008","article-title":"Complete classification of torsion of elliptic curves over quadratic cyclotomic fields","volume":"130","author":"Najman, Filip","year":"2010","journal-title":"J. Number Theory","ISSN":"https:\/\/id.crossref.org\/issn\/0022-314X","issn-type":"print"},{"issue":"1","key":"32","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1017\/S0305004117000160","article-title":"Isogenies of non-CM elliptic curves with rational \ud835\udc57-invariants over number fields","volume":"164","author":"Najman, Filip","year":"2018","journal-title":"Math. Proc. Cambridge Philos. Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0305-0041","issn-type":"print"},{"issue":"2","key":"33","doi-asserted-by":"publisher","first-page":"Paper No. 28, 18","DOI":"10.1007\/s40993-022-00325-w","article-title":"Splitting of primes in number fields generated by points on some modular curves","volume":"8","author":"Najman, Filip","year":"2022","journal-title":"Res. Number Theory","ISSN":"https:\/\/id.crossref.org\/issn\/2522-0160","issn-type":"print"},{"issue":"342","key":"34","doi-asserted-by":"publisher","first-page":"1791","DOI":"10.1090\/mcom\/3805","article-title":"Quadratic points on bielliptic modular curves","volume":"92","author":"Najman, Filip","year":"2023","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"319","key":"35","doi-asserted-by":"publisher","first-page":"2461","DOI":"10.1090\/mcom\/3407","article-title":"Quadratic points on modular curves","volume":"88","author":"Ozman, Ekin","year":"2019","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"4","key":"36","doi-asserted-by":"publisher","first-page":"323","DOI":"10.4064\/aa152-4-1","article-title":"Points on quadratic twists of \ud835\udc4b\u2080(\ud835\udc41)","volume":"152","author":"Ozman, Ekin","year":"2012","journal-title":"Acta Arith.","ISSN":"https:\/\/id.crossref.org\/issn\/0065-1036","issn-type":"print"},{"issue":"2","key":"37","doi-asserted-by":"publisher","first-page":"209","DOI":"10.2140\/ant.2009.3.209","article-title":"Chabauty for symmetric powers of curves","volume":"3","author":"Siksek, Samir","year":"2009","journal-title":"Algebra Number Theory","ISSN":"https:\/\/id.crossref.org\/issn\/1937-0652","issn-type":"print"},{"key":"38","unstructured":"[{The}20] The Sage Developers, SageMath, the Sage Mathematics Software System (Version 9.2), 2020. \\url{https:\/\/www.sagemath.org}."},{"key":"39","unstructured":"[{The}21] The PARI Group, Univ. Bordeaux. PARI\/GP version 2.14.0, 2021. available from \\url{http:\/\/pari.math.u-bordeaux.fr\/}."},{"issue":"2","key":"40","doi-asserted-by":"publisher","first-page":"141","DOI":"10.4064\/aa180725-8-1","article-title":"Torsion groups of elliptic curves over quadratic fields \u211a(\u221a\ud835\udd55), 0<\ud835\udd55<100","volume":"192","author":"Trbovi\u0107, Antonela","year":"2020","journal-title":"Acta Arith.","ISSN":"https:\/\/id.crossref.org\/issn\/0065-1036","issn-type":"print"},{"key":"41","unstructured":"[Vuk22] Borna Vukorepa, Isogenies over quadratic fields of elliptic curves with rational j-invariant, preprint, available at  arXiv:2203.10672, 2022."}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.ams.org\/mcom\/2024-93-346\/S0025-5718-2023-03894-7\/mcom3894_AM.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/www.ams.org\/mcom\/2024-93-346\/S0025-5718-2023-03894-7\/S0025-5718-2023-03894-7.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T05:13:23Z","timestamp":1776834803000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2024-93-346\/S0025-5718-2023-03894-7\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,8,30]]},"references-count":41,"journal-issue":{"issue":"346","published-print":{"date-parts":[[2024,3]]}},"alternative-id":["S0025-5718-2023-03894-7"],"URL":"https:\/\/doi.org\/10.1090\/mcom\/3894","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":[[2023,8,30]]}}}