{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T04:05:50Z","timestamp":1776830750724,"version":"3.51.2"},"reference-count":40,"publisher":"American Mathematical Society (AMS)","issue":"321","license":[{"start":{"date-parts":[[2020,4,30]],"date-time":"2020-04-30T00:00:00Z","timestamp":1588204800000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/501100003329","name":"Ministerio de Econom\u00c3\u00ada y Competitividad","doi-asserted-by":"publisher","award":["MTM2015-68524-P"],"award-info":[{"award-number":["MTM2015-68524-P"]}],"id":[{"id":"10.13039\/501100003329","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    Given an elliptic curve\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                    with torsion subgroup\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper G equals upper E left-parenthesis double-struck upper Q right-parenthesis Subscript left-brace tors right-brace\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>G<\/mml:mi>\n                            <mml:mo>=<\/mml:mo>\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:msub>\n                              <mml:mo stretchy=\"false\">)<\/mml:mo>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mtext>{tors}<\/mml:mtext>\n                              <\/mml:mrow>\n                            <\/mml:msub>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">G = E(\\mathbb {Q})_\\textrm {{tors}}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    we study what groups (up to isomorphism) can occur as 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\">\n                        <mml:semantics>\n                          <mml:mi>E<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">E<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    base-extended to\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper K\">\n                        <mml:semantics>\n                          <mml:mi>K<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">K<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    , a degree 6 extension 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                    . We also determine which groups\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper H equals upper E left-parenthesis upper K right-parenthesis Subscript left-brace tors right-brace\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>H<\/mml:mi>\n                            <mml:mo>=<\/mml:mo>\n                            <mml:mi>E<\/mml:mi>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>K<\/mml:mi>\n                            <mml:msub>\n                              <mml:mo stretchy=\"false\">)<\/mml:mo>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mtext>{tors}<\/mml:mtext>\n                              <\/mml:mrow>\n                            <\/mml:msub>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">H = E(K)_\\textrm {{tors}}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    can occur infinitely often and which ones occur for only finitely many curves. This article is a first step towards a complete classification of torsion growth over sextic fields.\n                  <\/p>","DOI":"10.1090\/mcom\/3440","type":"journal-article","created":{"date-parts":[[2019,3,13]],"date-time":"2019-03-13T09:41:55Z","timestamp":1552470115000},"page":"411-435","source":"Crossref","is-referenced-by-count":9,"title":["On the torsion of rational elliptic curves over sextic fields"],"prefix":"10.1090","volume":"89","author":[{"given":"Harris","family":"Daniels","sequence":"first","affiliation":[]},{"given":"Enrique","family":"Gonz\u00e1lez-Jim\u00e9nez","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2019,4,30]]},"reference":[{"key":"1","unstructured":"J. S. Balakrishnan, N. Dogra, J. S. M\u00fcller, J. Tuitman, and J. Vonk, Explicit Chabauty\u2013Kim for the split Cartan modular curve of level 13, arXiv:1711.05846, (2017). To appear in Ann. of Math."},{"key":"2","unstructured":"W. Bosma, J. Cannon, C. 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