Involutory elliptic curves over \(\mathbb{F}_q(T)\)
type: Item
instance of: scholarly article
title: Involutory elliptic curves over \(\mathbb{F}_q(T)\)
zbMATH Open document ID: 0930.11040
author: Andreas Schweizer
published in: Journal de Théorie des Nombres de Bordeaux
publication date: 1999-06-23T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/93704
full work available at URL: jtnb1998-1.html
review text: Let \(\mathbb{F}_q\) be a field with \(q\) elements, \(n\in\mathbb{F}_q[T]-\{0\}\) and \(G\) be a subgroup of the Atkin-Lehner involutions of the Drinfeld modular curve \(X_0(n)\). The author determines all \(n\) and \(G\) such that the quotient curve \(G\setminus X_0(n)\) is rational or elliptic. This problem is related, as suggested in the title, to the classical (and solved) problem on involutory elliptic curves. Interesting calculations about the genus of \(G\setminus X_0(n)\) are done in \S 2.
Mathematics Subject Classification ID: 11G18
Mathematics Subject Classification ID: 11G05
Mathematics Subject Classification ID: 11G09
zbMATH DE Number: 1229650
zbMATH Keywords: Drinfeld modular curve
zbMATH Keywords: involutory elliptic curves
zbMATH Keywords: genus
reviewed by: Marc Reversat
MaRDI profile type: Publication
OpenAlex ID: W2320410176
cites work: Hecke operators on \(\Gamma_0(m)\)
cites work: Q3890820
cites work: Automorphe Formen über \({\mathbb{F}}_ q(T)\) mit kleinem Führer. (Automorphic forms over \({\mathbb{F}}_ q(T)\) with small conductor)
cites work: Analytical construction of Weil curves over function fields
cites work: FUNDAMENTAL DOMAINS OF SOME ARITHMETIC GROUPS OVER FUNCTION FIELDS
cites work: Jacobians of Drinfeld modular curves.
cites work: A NOTE ON INVOLUTORY WEIL CURVES
cites work: Q4126408
cites work: Arithmetic of Weil curves
cites work: Modular automorphisms of the Drinfeld modular curves \(X_ 0 ({\mathfrak n})\)
cites work: Q4234809
DOI: 10.5802/JTNB.221
description: scientific article; zbMATH DE number 1229650