{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T06:02:01Z","timestamp":1776837721080,"version":"3.51.2"},"reference-count":27,"publisher":"American Mathematical Society (AMS)","issue":"346","license":[{"start":{"date-parts":[[2024,7,13]],"date-time":"2024-07-13T00:00:00Z","timestamp":1720828800000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/501100004488","name":"Hrvatska Zaklada za Znanost","doi-asserted-by":"publisher","award":["P-2018-01-1313"],"award-info":[{"award-number":["P-2018-01-1313"]}],"id":[{"id":"10.13039\/501100004488","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004488","name":"Hrvatska Zaklada za Znanost","doi-asserted-by":"publisher","award":["KK.01.1.1.01.0004"],"award-info":[{"award-number":["KK.01.1.1.01.0004"]}],"id":[{"id":"10.13039\/501100004488","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100016125","name":"Cohesion Fund","doi-asserted-by":"publisher","award":["P-2018-01-1313"],"award-info":[{"award-number":["P-2018-01-1313"]}],"id":[{"id":"10.13039\/501100016125","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100016125","name":"Cohesion Fund","doi-asserted-by":"publisher","award":["KK.01.1.1.01.0004"],"award-info":[{"award-number":["KK.01.1.1.01.0004"]}],"id":[{"id":"10.13039\/501100016125","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004488","name":"Hrvatska Zaklada za Znanost","doi-asserted-by":"publisher","award":["P-2018-01-1313"],"award-info":[{"award-number":["P-2018-01-1313"]}],"id":[{"id":"10.13039\/501100004488","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004488","name":"Hrvatska Zaklada za Znanost","doi-asserted-by":"publisher","award":["KK.01.1.1.01.0004"],"award-info":[{"award-number":["KK.01.1.1.01.0004"]}],"id":[{"id":"10.13039\/501100004488","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"

\n In this paper we determine the\n \n \n \n \n Q<\/mml:mi>\n <\/mml:mrow>\n \\mathbb {Q}<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n -gonalities of the modular curves\n \n \n \n \n \n X<\/mml:mi>\n 0<\/mml:mn>\n <\/mml:msub>\n (<\/mml:mo>\n N<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n X_0(N)<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n for all\n \n \n \n \n N<\/mml:mi>\n ><\/mml:mo>\n 145<\/mml:mn>\n <\/mml:mrow>\n N>145<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n . We determine the\n \n \n \n \n C<\/mml:mi>\n <\/mml:mrow>\n \\mathbb {C}<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n -gonality of many of these curves and the\n \n \n \n \n Q<\/mml:mi>\n <\/mml:mrow>\n \\mathbb {Q}<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n -gonalities and\n \n \n \n \n C<\/mml:mi>\n <\/mml:mrow>\n \\mathbb {C}<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n -gonalities for many larger values of\n \n \n \n N<\/mml:mi>\n N<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n .\n <\/p>\n

\n Using these results and some further work, we determine all the modular curves\n \n \n \n \n \n X<\/mml:mi>\n 0<\/mml:mn>\n <\/mml:msub>\n (<\/mml:mo>\n N<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n X_0(N)<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n of gonality\n \n \n \n 4<\/mml:mn>\n 4<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n ,\n \n \n \n 5<\/mml:mn>\n 5<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n and\n \n \n \n 6<\/mml:mn>\n 6<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n over\n \n \n \n \n Q<\/mml:mi>\n <\/mml:mrow>\n \\mathbb {Q}<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n . We also find the first known instances of pentagonal curves\n \n \n \n \n \n X<\/mml:mi>\n 0<\/mml:mn>\n <\/mml:msub>\n (<\/mml:mo>\n N<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n X_0(N)<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n over\n \n \n \n \n C<\/mml:mi>\n <\/mml:mrow>\n \\mathbb {C}<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n .\n <\/p>","DOI":"10.1090\/mcom\/3873","type":"journal-article","created":{"date-parts":[[2023,5,24]],"date-time":"2023-05-24T09:35:05Z","timestamp":1684920905000},"page":"863-886","source":"Crossref","is-referenced-by-count":3,"title":["Gonality of the modular curve \ud835\udc4b\u2080(\ud835\udc41)"],"prefix":"10.1090","volume":"93","author":[{"given":"Filip","family":"Najman","sequence":"first","affiliation":[]},{"given":"Petar","family":"Orli\u0107","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2023,7,13]]},"reference":[{"issue":"20","key":"1","doi-asserted-by":"publisher","first-page":"1005","DOI":"10.1155\/S1073792896000621","article-title":"A linear lower bound on the gonality of modular curves","author":"Abramovich, Dan","year":"1996","journal-title":"Internat. 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