{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,4]],"date-time":"2026-07-04T21:16:02Z","timestamp":1783199762095,"version":"3.54.6"},"reference-count":37,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","award":["23K03199"],"award-info":[{"award-number":["23K03199"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Finite Fields and Their Applications"],"published-print":{"date-parts":[[2026,10]]},"DOI":"10.1016\/j.ffa.2026.102859","type":"journal-article","created":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T16:23:47Z","timestamp":1780676627000},"page":"102859","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Generalised Howe curves of genus five attaining the Serre bound"],"prefix":"10.1016","volume":"115","author":[{"given":"Motoko Qiu","family":"Kawakita","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/j.ffa.2026.102859_br0010","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1016\/S0022-314X(01)92760-X","article-title":"Legendre elliptic curves over finite field","volume":"95","author":"Auer","year":"2002","journal-title":"J. Number Theory"},{"key":"10.1016\/j.ffa.2026.102859_br0020","author":"Booher"},{"key":"10.1016\/j.ffa.2026.102859_br0030","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1006\/jsco.1996.0125","article-title":"The Magma algebra system. I. The user language","volume":"24","author":"Bosma","year":"1997","journal-title":"J. Symb. Comput."},{"key":"10.1016\/j.ffa.2026.102859_br0040","series-title":"PQCrypto 2020","first-page":"151","article-title":"The supersingular isogeny problem in genus 2 and beyond","volume":"vol. 12100","author":"Costello","year":"2020"},{"key":"10.1016\/j.ffa.2026.102859_br0050","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1007\/BF02940746","article-title":"Die Typen der Multiplicatorenringe elliptischer Funktionen-k\u00f6rper","volume":"14","author":"Deuring","year":"1941","journal-title":"Abh. Math. Semin. Univ. Hamb."},{"key":"10.1016\/j.ffa.2026.102859_br0060","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1007\/BF01388985","article-title":"The existence of infinitely many supersingular primes for every elliptic curve over Q","volume":"89","author":"Elkies","year":"1987","journal-title":"Invent. Math."},{"issue":"3","key":"10.1016\/j.ffa.2026.102859_br0070","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1515\/advgeom.2010.020","article-title":"A generalization of the Giulietti\u2013Korchm\u00e1ros maximal curve","volume":"10","author":"Garcia","year":"2010","journal-title":"Adv. Geom."},{"issue":"39","key":"10.1016\/j.ffa.2026.102859_br0080","doi-asserted-by":"crossref","first-page":"199","DOI":"10.4064\/aa135-3-1","article-title":"Certain maximal curves and Cartier operators","volume":"135","author":"Garcia","year":"2008","journal-title":"Acta Arith."},{"key":"10.1016\/j.ffa.2026.102859_br0090","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1016\/0097-3165(95)90099-3","article-title":"Fibre products of Artin\u2013Schreier curves and generalized Hamming weights of codes","volume":"70","author":"van der Geer","year":"1995","journal-title":"J. Comb. Theory, Ser. A"},{"key":"10.1016\/j.ffa.2026.102859_br0100","author":"van der Geer"},{"key":"10.1016\/j.ffa.2026.102859_br0110","doi-asserted-by":"crossref","first-page":"145","DOI":"10.4064\/aa170406-30-1","article-title":"An average asymptotic for the number of extremal primes of elliptic curves","volume":"183","author":"Giberson","year":"2018","journal-title":"Acta Arith."},{"issue":"4","key":"10.1016\/j.ffa.2026.102859_br0120","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1515\/advgeom-2020-0012","article-title":"An Fp2-maximal Wiman sextic and its automorphisms","volume":"21","author":"Giulietti","year":"2021","journal-title":"Adv. Geom."},{"key":"10.1016\/j.ffa.2026.102859_br0130","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1016\/j.ffa.2016.05.005","article-title":"On maximal curves that are not quotients of the Hermitian curve","volume":"41","author":"Giulietti","year":"2016","journal-title":"Finite Fields Appl."},{"issue":"6","key":"10.1016\/j.ffa.2026.102859_br0140","first-page":"1289","article-title":"Codes on algebraic curves","volume":"259","author":"Goppa","year":"1981","journal-title":"Dokl. Akad. Nauk SSSR"},{"key":"10.1016\/j.ffa.2026.102859_br0150","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1090\/conm\/574\/11431","article-title":"New bounds on the maximum number of points on genus-4 curves over small finite fields","volume":"574","author":"Howe","year":"2012","journal-title":"Contemp. Math."},{"key":"10.1016\/j.ffa.2026.102859_br0160","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1090\/conm\/663\/13353","article-title":"Quickly constructing curves of genus 4 with many points","volume":"663","author":"Howe","year":"2016","journal-title":"Contemp. Math."},{"key":"10.1016\/j.ffa.2026.102859_br0170","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1016\/j.ffa.2017.06.006","article-title":"Curves of medium genus with many points","volume":"47","author":"Howe","year":"2017","journal-title":"Finite Fields Appl."},{"issue":"1","key":"10.1016\/j.ffa.2026.102859_br0180","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1515\/advgeom-2023-0031","article-title":"New sextics of genus 6 and 10 attaining the Serre bound","volume":"24","author":"Iezzi","year":"2024","journal-title":"Adv. Geom."},{"key":"10.1016\/j.ffa.2026.102859_br0190","first-page":"721","article-title":"Some remarks on the number of rational points of algebraic curves over finite fields","volume":"28","author":"Ihara","year":"1981","journal-title":"J. Fac. Univ. Tokyo"},{"key":"10.1016\/j.ffa.2026.102859_br0200","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1016\/j.jnt.2016.09.033","article-title":"Extremal primes for elliptic curves with complex multiplication","volume":"172","author":"James","year":"2017","journal-title":"J. Number Theory"},{"issue":"2","key":"10.1016\/j.ffa.2026.102859_br0210","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1007\/BF01442878","article-title":"Idempotent relations and factors of Jacobians","volume":"284","author":"Kani","year":"1989","journal-title":"Math. Ann."},{"key":"10.1016\/j.ffa.2026.102859_br0220","series-title":"ANTS 2020","first-page":"283","article-title":"Counting Richelot isogenies between superspecial abelian surfaces","volume":"vol. 4","author":"Katsura","year":"2020"},{"key":"10.1016\/j.ffa.2026.102859_br0230","first-page":"3","article-title":"Decomposed Richelot isogenies of Jacobian varieties of hyperelliptic curves and generalized Howe curves","volume":"72","author":"Katsura","year":"2024","journal-title":"Comment. Math. Univ. St. Pauli"},{"issue":"3","key":"10.1016\/j.ffa.2026.102859_br0240","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1080\/10586458.2010.10390623","article-title":"2, 3, 5, Legendre: \u00b1trace ratio in families of elliptic curves","volume":"19","author":"Katz","year":"2010","journal-title":"Exp. Math."},{"issue":"2","key":"10.1016\/j.ffa.2026.102859_br0250","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1142\/S0219498805001058","article-title":"A quotient curve of the Fermat curve of degree twelve attaining the Serre bound","volume":"4","author":"Kawakita","year":"2005","journal-title":"J. Algebra Appl."},{"issue":"1","key":"10.1016\/j.ffa.2026.102859_br0260","doi-asserted-by":"crossref","first-page":"330","DOI":"10.1007\/s40879-017-0147-3","article-title":"Wiman's and Edge's sextic attaining Serre's bound","volume":"4","author":"Kawakita","year":"2017","journal-title":"Eur. J. Math."},{"key":"10.1016\/j.ffa.2026.102859_br0270","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1090\/conm\/637\/12758","article-title":"Wiman's and Edge's sextic attaining Serre's bound II","volume":"637","author":"Kawakita","year":"2015","journal-title":"Contemp. Math."},{"key":"10.1016\/j.ffa.2026.102859_br0280","doi-asserted-by":"crossref","first-page":"264","DOI":"10.1007\/978-3-030-05153-2_15","article-title":"Some sextics of genera five and seven attaining the Serre bound","volume":"11321","author":"Kawakita","year":"2018","journal-title":"Lect. Notes Comput. Sci."},{"key":"10.1016\/j.ffa.2026.102859_br0290","author":"Kudo"},{"key":"10.1016\/j.ffa.2026.102859_br0300","series-title":"ANTS 2020","first-page":"301","article-title":"Algorithms to enumerate superspecial Howe curves of genus four","volume":"vol. 4","author":"Kudo","year":"2020"},{"key":"10.1016\/j.ffa.2026.102859_br0310","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1007\/s40993-020-00217-x","article-title":"The existence of supersingular curves of genus 4 in arbitrary characteristic","volume":"6","author":"Kudo","year":"2020","journal-title":"Res. Number Theory"},{"key":"10.1016\/j.ffa.2026.102859_br0320","article-title":"Frobenius Distributions in GL2-Extensions","volume":"vol. 504","author":"Lang","year":"1976"},{"issue":"9","key":"10.1016\/j.ffa.2026.102859_br0330","first-page":"397","article-title":"Sur le nombre des points rationnels d'une courbe alg\u00e9brique sur un corps fini","volume":"296","author":"Serre","year":"1983","journal-title":"C. R. Acad. Sci. Paris, S\u00e9r. I Math."},{"key":"10.1016\/j.ffa.2026.102859_br0340","author":"Serre","year":"2020","journal-title":"Soc. Math. Fr."},{"key":"10.1016\/j.ffa.2026.102859_br0350","article-title":"The Arithmetic of Elliptic Curves","volume":"vol. 106","author":"Silverman","year":"2009"},{"key":"10.1016\/j.ffa.2026.102859_br0360","article-title":"Algebraic Function Fields and Codes","volume":"vol. 254","author":"Stichtenoth","year":"2009"},{"key":"10.1016\/j.ffa.2026.102859_br0370","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1007\/BF01404549","article-title":"Endomorphisms of Abelian varieties over finite fields","volume":"2","author":"Tate","year":"1966","journal-title":"Invent. Math."}],"container-title":["Finite Fields and Their Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S1071579726000705?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S1071579726000705?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,7,4]],"date-time":"2026-07-04T20:34:07Z","timestamp":1783197247000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S1071579726000705"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,10]]},"references-count":37,"alternative-id":["S1071579726000705"],"URL":"https:\/\/doi.org\/10.1016\/j.ffa.2026.102859","relation":{},"ISSN":["1071-5797"],"issn-type":[{"value":"1071-5797","type":"print"}],"subject":[],"published":{"date-parts":[[2026,10]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Generalised Howe curves of genus five attaining the Serre bound","name":"articletitle","label":"Article Title"},{"value":"Finite Fields and Their Applications","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.ffa.2026.102859","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"102859"}}