{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T05:41:11Z","timestamp":1776836471190,"version":"3.51.2"},"reference-count":54,"publisher":"American Mathematical Society (AMS)","issue":"339","license":[{"start":{"date-parts":[[2023,8,22]],"date-time":"2023-08-22T00:00:00Z","timestamp":1692662400000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/501100003542","name":"Ministerium f\u00fcr Wissenschaft, Forschung und Kunst Baden-W\u00fcrttemberg","doi-asserted-by":"publisher","award":["811340"],"award-info":[{"award-number":["811340"]}],"id":[{"id":"10.13039\/501100003542","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003542","name":"Ministerium f\u00fcr Wissenschaft, Forschung und Kunst Baden-W\u00fcrttemberg","doi-asserted-by":"publisher","award":["438058067"],"award-info":[{"award-number":["438058067"]}],"id":[{"id":"10.13039\/501100003542","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["811340"],"award-info":[{"award-number":["811340"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["438058067"],"award-info":[{"award-number":["438058067"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    We analyze complex multiplication for Jacobians of curves of genus 3, as well as the resulting Shimura class groups and their subgroups corresponding to Galois conjugation over the reflex field. We combine our results with numerical methods to find CM fields\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                    for which there exist both hyperelliptic and non-hyperelliptic curves whose Jacobian has complex multiplication by\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"double-struck upper Z Subscript upper K\">\n                        <mml:semantics>\n                          <mml:msub>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mi mathvariant=\"double-struck\">Z<\/mml:mi>\n                            <\/mml:mrow>\n                            <mml:mi>K<\/mml:mi>\n                          <\/mml:msub>\n                          <mml:annotation encoding=\"application\/x-tex\">\\mathbb {Z}_K<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . More precisely, we find all sextic CM fields\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                    in the LMFDB for which (heuristically) Jacobians of both types with CM by\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"double-struck upper Z Subscript upper K\">\n                        <mml:semantics>\n                          <mml:msub>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mi mathvariant=\"double-struck\">Z<\/mml:mi>\n                            <\/mml:mrow>\n                            <mml:mi>K<\/mml:mi>\n                          <\/mml:msub>\n                          <mml:annotation encoding=\"application\/x-tex\">\\mathbb {Z}_K<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    exist. There turn out to be 14 such fields among the 547,156 sextic CM fields that the LMFDB contains. We determine invariants of the corresponding curves, and in the simplest case we also give an explicit defining equation.\n                  <\/p>","DOI":"10.1090\/mcom\/3776","type":"journal-article","created":{"date-parts":[[2022,8,10]],"date-time":"2022-08-10T15:16:30Z","timestamp":1660144590000},"page":"349-383","source":"Crossref","is-referenced-by-count":2,"title":["Isogenous hyperelliptic and non-hyperelliptic Jacobians with maximal complex multiplication"],"prefix":"10.1090","volume":"92","author":[{"given":"Bogdan","family":"Dina","sequence":"first","affiliation":[]},{"given":"Sorina","family":"Ionica","sequence":"additional","affiliation":[]},{"given":"Jeroen","family":"Sijsling","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2022,8,22]]},"reference":[{"key":"1","doi-asserted-by":"publisher","first-page":"283","DOI":"10.1112\/S1461157016000322","article-title":"Constructing genus-3 hyperelliptic Jacobians with CM","volume":"19","author":"Balakrishnan, Jennifer S.","year":"2016","journal-title":"LMS J. 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