Singularities of the Modular Curve
Finite Fields and their Applications
415 - 420
MetadataShow full item record
Please cite this item using this persistent URLhttp://hdl.handle.net/11693/24840
Let X0(ℓ) be the modular curve, parameterizing cyclic isogenies of degree ℓ, and Z0(ℓ) be its plane model, given by the classical modular equation Φℓ(X, Y)=0. We prove that all singularities of Z0(ℓ), except two cusps, are intersections of smooth branches, and evaluate the order of contact of these branches. © 2001 Academic Press.