On Siegel's modular curve of level 5 and the class number one problem
type: Item
instance of: scholarly article
title: On Siegel's modular curve of level 5 and the class number one problem
zbMATH Open document ID: 0916.11036
author: Imin Chen
published in: Journal of Number Theory
publication date: 1999-06-20T00:00:00Z
review text: Given a prime \(p\), let \(z\) be an element of \(\mathbb P (\mathbb F_{p^2})\) with \(z \notin \mathbb P (\mathbb F_p)\), and let \(N_z\) be the stabilizer of \(\{ z. z^p \}\) in \(GL_2 (\mathbb F_p)\). If \(X(p)\) denotes the modular curve which classifies isomorphism classes of elliptic curves with level \(p\) structure, then \(X^+_{\text{ns}} (p)\) is the quotient of \(X(p)\) by \(N_z \subset GL_2 (\mathbb F_p)\). An explicit parametrization of \(X^+_{\text{ns}} (5)\) was obtained by \textit{C. L. Siegel} [Invent. Math. 5, 180-191 (1968; Zbl 0175.33602)] and was used to solve the class number one problem. In this paper the author derives another explicit parametrization of the modular curve \(X^+_{\text{ns}} (5)\) over \(\mathbb Q\).
reviewed by: Min Ho Lee
Mathematics Subject Classification ID: 11G30
Mathematics Subject Classification ID: 11R29
Mathematics Subject Classification ID: 11G07
Mathematics Subject Classification ID: 14G35
zbMATH DE Number: 1271092
zbMATH Keywords: modular curves
zbMATH Keywords: class numbers
zbMATH Keywords: elliptic curves
Wikidata QID: Q56017689
MaRDI profile type: Publication
OpenAlex ID: W2059095021
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DOI: 10.1006/JNTH.1998.2320
description: scientific article; zbMATH DE number 1271092