Computing modular degrees using \(L\)-functions
type: Item
instance of: scholarly article
title: Computing modular degrees using \(L\)-functions
zbMATH Open document ID: 1070.11021
author: C. Delaunay
published in: Journal de Théorie des Nombres de Bordeaux
publication date: 2005-06-30T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/93909
review text: Let \(E\) be an elliptic curve of conductor \(N\) defined over \(\mathbb Q\). There exists a modular parametrization \(\varphi\) from \(X_0(N)\) to \(E.\) By results of \textit{D. Zagier} [Can. Math. Bull. 28, 372--384 (1985; Zbl 0579.14027)] and \textit{G. Shimura} [Pure Appl. Math. 29, 783--804 (1976; Zbl 0348.10015)] one can compute the degree of \(\varphi\) once the critical value \(L(\text{Sym}^2(E),2)\) is known. The author proposes an algorithm which calculates this value and seems to be faster than \textit{J. E. Cremona}'s [Algorithms for modular elliptic curves, Cambridge University Press (1997; Zbl 0872.14041)], at least for large conductor.
reviewed by: Stefan Kühnlein
Mathematics Subject Classification ID: 11F67
Mathematics Subject Classification ID: 11G05
zbMATH DE Number: 2184618
zbMATH Keywords: modular parametrization
zbMATH Keywords: elliptic curve
zbMATH Keywords: symmetric square
describes a project that uses: ecdata
MaRDI profile type: Publication
OpenAlex ID: W2022659769
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DOI: 10.5802/JTNB.420
description: scientific article; zbMATH DE number 2184618