{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T15:16:32Z","timestamp":1776870992544,"version":"3.51.2"},"reference-count":39,"publisher":"American Mathematical Society (AMS)","issue":"292","license":[{"start":{"date-parts":[[2015,7,29]],"date-time":"2015-07-29T00:00:00Z","timestamp":1438128000000},"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                    This is the third in a series of papers in which we study the\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"n\">\n                        <mml:semantics>\n                          <mml:mi>n<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">n<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -Selmer group of an elliptic curve, with the aim of representing its elements as curves of degree\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"n\">\n                        <mml:semantics>\n                          <mml:mi>n<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">n<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    in\u00a0\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"double-struck upper P Superscript n minus 1\">\n                        <mml:semantics>\n                          <mml:msup>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mi mathvariant=\"double-struck\">P<\/mml:mi>\n                            <\/mml:mrow>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mi>n<\/mml:mi>\n                              <mml:mo>\n                                \u2212\n                                \n                              <\/mml:mo>\n                              <mml:mn>1<\/mml:mn>\n                            <\/mml:mrow>\n                          <\/mml:msup>\n                          <mml:annotation encoding=\"application\/x-tex\">\\mathbb {P}^{n-1}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . The methods we describe are practical in the case\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"n equals 3\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>n<\/mml:mi>\n                            <mml:mo>=<\/mml:mo>\n                            <mml:mn>3<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">n=3<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    for elliptic curves over the rationals, and have been implemented in\n                    <sans-serif>MAGMA<\/sans-serif>\n                    .\n                  <\/p>\n                  <p>One important ingredient of our work is an algorithm for trivialising central simple algebras. This is of independent interest; for example, it could be used for parametrising Brauer-Severi surfaces.<\/p>","DOI":"10.1090\/s0025-5718-2014-02858-5","type":"journal-article","created":{"date-parts":[[2014,7,29]],"date-time":"2014-07-29T08:20:21Z","timestamp":1406622021000},"page":"895-922","source":"Crossref","is-referenced-by-count":11,"title":["Explicit \ud835\udc5b-descent on elliptic curves III. 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