Singularities of the modular curve

Authors
Klyachko, A Kara, O
Citation
A. Klyachko et O. Kara, Singularities of the modular curve, FINITE F T, 7(3), 2001, pp. 415-420
Citations number
6
Categorie Soggetti
Mathematics
Journal title
FINITE FIELDS AND THEIR APPLICATIONS
ISSN journal
10715797 → ACNP
Volume
7
Issue
3
Year of publication
2001
Pages
415 - 420
Database
ISI
SICI code
1071-5797(200107)7:3<415:SOTMC>2.0.ZU;2-P
Abstract
Let X-0(l) be the modular curve, parameterizing cyclic isogenies of degree l, and Z(0)(l) be its plane model, given by the classical modular equation Phi (l)(X, Y) = 0. We prove that all singularities of Z(0)(l), except two c usps, are intersections of smooth branches, and evaluate the order of conta ct of these branches. (C) 2001 Academic Press.