Parameterization of algebraic points of a given degree on the curve of the affine equation \(y^3=x(x - 1)(x - 2)(x - 3)\)
type: Item
instance of: scholarly article
title: Parameterization of algebraic points of a given degree on the curve of the affine equation \(y^3=x(x - 1)(x - 2)(x - 3)\)
zbMATH Open document ID: 1218.11066
author: Oumar Sall
author: Thiéyacine Top
author: Moussa Fall
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2010-12-14T00:00:00Z
review text: \textit{E. F. Schaefer} [Math. Ann. 310, No. 3, 447--471 (1998; Zbl 0889.11021)] described the algebraic points of degree 2 and 3 on the curve \(C : y^3 = x(x-1)(x-2)(x-3)\) over \(\mathbb{Q}\). By using the computation of the Mordell-Weil group of the Jacobian of \(C\), the Abel-Jacobi theorem, and the study of linear systems on \(C\), the authors generalize the mentioned description to algebraic points of any given degree. The result is very explicit for degrees \(\leq 5\).
reviewed by: Vasyl I. Andriychuk
Mathematics Subject Classification ID: 11G30
Mathematics Subject Classification ID: 14G25
Mathematics Subject Classification ID: 14H25
Mathematics Subject Classification ID: 14H45
zbMATH DE Number: 5826225
zbMATH Keywords: curves over global fields
zbMATH Keywords: Jacobian
zbMATH Keywords: Mordell-Weil group
MaRDI profile type: Publication
full work available at URL: j.crma.2010.10.023
OpenAlex ID: W2019210571
cites work: Computing a Selmer group of a Jacobian using functions on the curve
cites work: Some results on the Mordell-Weil group of the Jacobian of the Fermat curve
DOI: 10.1016/J.CRMA.2010.10.023
description: scientific article; zbMATH DE number 5826225