Nonsingular plane cubic curves over finite fields
type: Item
instance of: scholarly article
title: Nonsingular plane cubic curves over finite fields
zbMATH Open document ID: 0632.14021
DOI: 10.1016/0097-3165(87)90003-3
author: René Schoof
published in: Journal of Combinatorial Theory. Series A
publication date: 1987-01-01T00:00:00Z
review text: Der Autor berechnet die Anzahl der projektiv inäquivalenten, nichtsingulären, ebenen Kurven vom Grad 3 über einem endlichen Körper \({\mathbb{F}}_ q\), oder anders formuliert, die Anzahl der Isomorphieklassen von elliptischen Kurven und deren Einbettung in den zweidimensionalen projektiven Raum vom Grad 3. Ein wichtiger Punkt bei diesen Rechnungen ist die Kenntnis aller Ordnungen (und deren Klassenzahlen), die als Endomorphismenringe von elliptischen Kurven über \({\mathbb{F}}_ q\) auftreten; siehe dazu: \textit{M. Deuring} [Abh. Math. Sem. Hansische Univ. 14, 197-272 (1941; Zbl 0025.02003)] und \textit{W. C. Waterhouse} [Ann. Sci. Éc. Norm. Supér., IV. Sér. 2(1969), 521-560 (1970; Zbl 0188.530)].
Mathematics Subject Classification ID: 14G15
Mathematics Subject Classification ID: 14H45
Mathematics Subject Classification ID: 14H52
zbMATH DE Number: 4027654
zbMATH Keywords: number of nonsingular plane elliptic curves
zbMATH Keywords: finite ground field
MaRDI profile type: Publication
full work available at URL: 0097-3165(87)90003-3
OpenAlex ID: W2098377074
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description: scientific article; zbMATH DE number 4027654