{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T22:32:31Z","timestamp":1777674751849,"version":"3.51.4"},"reference-count":29,"publisher":"American Mathematical Society (AMS)","issue":"266","license":[{"start":{"date-parts":[[2009,8,14]],"date-time":"2009-08-14T00:00:00Z","timestamp":1250208000000},"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":"

\n We enumerate all Shimura curves\n \n \n \n \n \n X<\/mml:mi>\n 0<\/mml:mn>\n \n \n D<\/mml:mi>\n <\/mml:mrow>\n <\/mml:mrow>\n <\/mml:msubsup>\n (<\/mml:mo>\n \n N<\/mml:mi>\n <\/mml:mrow>\n )<\/mml:mo>\n <\/mml:mrow>\n X^{\\mathfrak {D}}_0(\\mathfrak {N})<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n of genus at most two: there are exactly 858 such curves, up to equivalence.\n <\/p>","DOI":"10.1090\/s0025-5718-08-02163-7","type":"journal-article","created":{"date-parts":[[2009,12,1]],"date-time":"2009-12-01T13:09:23Z","timestamp":1259672963000},"page":"1155-1172","source":"Crossref","is-referenced-by-count":22,"title":["Shimura curves of genus at most two"],"prefix":"10.1090","volume":"78","author":[{"given":"John","family":"Voight","sequence":"first","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2008,8,14]]},"reference":[{"key":"1","series-title":"CRM Monograph Series","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1090\/crmm\/022","volume-title":"Quaternion orders, quadratic forms, and Shimura curves","volume":"22","author":"Alsina, Montserrat","year":"2004","ISBN":"https:\/\/id.crossref.org\/isbn\/0821833596"},{"issue":"1","key":"2","doi-asserted-by":"publisher","first-page":"408","DOI":"10.1016\/j.jalgebra.2004.02.025","article-title":"On Rademacher\u2019s conjecture: congruence subgroups of genus zero of the modular group","volume":"277","author":"Chua, Kok Seng","year":"2004","journal-title":"J. Algebra","ISSN":"https:\/\/id.crossref.org\/issn\/0021-8693","issn-type":"print"},{"key":"3","series-title":"Graduate Texts in Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-8489-0","volume-title":"Advanced topics in computational number theory","volume":"193","author":"Cohen, Henri","year":"2000","ISBN":"https:\/\/id.crossref.org\/isbn\/0387987274"},{"issue":"242","key":"4","doi-asserted-by":"publisher","first-page":"941","DOI":"10.1090\/S0025-5718-02-01452-7","article-title":"Constructing complete tables of quartic fields using Kummer theory","volume":"72","author":"Cohen, Henri","year":"2003","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"5","unstructured":"J\u00e1nos A. Csirik, Joseph L. Wetherell, and Michael E. Zieve, On the genera of \ud835\udc4b\u2080(\ud835\udc41), to appear in J. Number Theory, math.NT\/0006096."},{"key":"6","series-title":"Graduate Texts in Mathematics","isbn-type":"print","volume-title":"A first course in modular forms","volume":"228","author":"Diamond, Fred","year":"2005","ISBN":"https:\/\/id.crossref.org\/isbn\/038723229X"},{"issue":"2","key":"7","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1080\/10586458.2004.10504528","article-title":"Computing special values of motivic \ud835\udc3f-functions","volume":"13","author":"Dokchitser, Tim","year":"2004","journal-title":"Experiment. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/1058-6458","issn-type":"print"},{"key":"8","isbn-type":"print","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/BFb0054850","article-title":"Shimura curve computations","author":"Elkies, Noam D.","year":"1998","ISBN":"https:\/\/id.crossref.org\/isbn\/3540646574"},{"key":"9","series-title":"Lecture Notes in Mathematics, Vol. 114","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0058988","volume-title":"Automorphic forms on ${\\rm GL}(2)$","author":"Jacquet, H.","year":"1970"},{"issue":"2","key":"10","doi-asserted-by":"publisher","first-page":"171","DOI":"10.4064\/aa-86-2-171-191","article-title":"Genera of arithmetic Fuchsian groups","volume":"86","author":"Johansson, Stefan","year":"1998","journal-title":"Acta Arith.","ISSN":"https:\/\/id.crossref.org\/issn\/0065-1036","issn-type":"print"},{"key":"11","series-title":"Chicago Lectures in Mathematics","isbn-type":"print","volume-title":"Fuchsian groups","author":"Katok, Svetlana","year":"1992","ISBN":"https:\/\/id.crossref.org\/isbn\/0226425827"},{"issue":"2","key":"12","doi-asserted-by":"publisher","first-page":"569","DOI":"10.4310\/PAMQ.2006.v2.n2.a9","article-title":"Arithmetic Fuchsian groups of genus zero","volume":"2","author":"Long, D. D.","year":"2006","journal-title":"Pure Appl. Math. Q.","ISSN":"https:\/\/id.crossref.org\/issn\/1558-8599","issn-type":"print"},{"issue":"219","key":"13","doi-asserted-by":"publisher","first-page":"1185","DOI":"10.1090\/S0025-5718-97-00863-6","article-title":"Computation of relative class numbers of CM-fields","volume":"66","author":"Louboutin, St\u00e9phane","year":"1997","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"1","key":"14","doi-asserted-by":"publisher","first-page":"7","DOI":"10.1017\/S0305004100075113","article-title":"Two-generator arithmetic Fuchsian groups. II","volume":"111","author":"Maclachlan, C.","year":"1992","journal-title":"Math. Proc. Cambridge Philos. Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0305-0041","issn-type":"print"},{"key":"15","isbn-type":"print","first-page":"151","article-title":"Petits discriminants des corps de nombres","author":"Martinet, Jacques","year":"1982","ISBN":"https:\/\/id.crossref.org\/isbn\/0521285135"},{"issue":"1","key":"16","doi-asserted-by":"crossref","first-page":"119","DOI":"10.5802\/jtnb.22","article-title":"Bounds for discriminants and related estimates for class numbers, regulators and zeros of zeta functions: a survey of recent results","volume":"2","author":"Odlyzko, A. M.","year":"1990","journal-title":"S\\'{e}m. Th\\'{e}or. 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Ann.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5831","issn-type":"print"},{"key":"19","first-page":"1","article-title":"On the estimation of Fourier coefficients of modular forms","author":"Selberg, Atle","year":"1965"},{"key":"20","doi-asserted-by":"publisher","first-page":"166","DOI":"10.2307\/1970389","article-title":"On zeta functions of quaternion algebras","volume":"81","author":"Shimizu, Hideo","year":"1965","journal-title":"Ann. of Math. (2)","ISSN":"https:\/\/id.crossref.org\/issn\/0003-486X","issn-type":"print"},{"issue":"2","key":"21","doi-asserted-by":"publisher","first-page":"443","DOI":"10.3836\/tjm\/1270043475","article-title":"Defining equations of modular curves \ud835\udc4b\u2080(\ud835\udc41)","volume":"18","author":"Shimura, Mahoro","year":"1995","journal-title":"Tokyo J. 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Sci, vol. 5011, Springer, Berlin, 2008, 268\u2013281.","DOI":"10.1007\/978-3-540-79456-1_18"},{"key":"27","unstructured":"John Voight, Shimura curves of genus at most two, http:\/\/www.cems.uvm.edu\/\u02dcvoight\/shim-tables\/ ."},{"key":"28","unstructured":"John Voight, Computing fundamental domains for Fuchsian groups, submitted to J. Th\u00e9orie de Nombres de Bordeaux."},{"key":"29","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1515\/crll.1991.414.113","article-title":"A spectral proof of Rademacher\u2019s conjecture for congruence subgroups of the modular group","volume":"414","author":"Zograf, P.","year":"1991","journal-title":"J. Reine Angew. 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