Author/Authors :
Alexander Klyachko، نويسنده , , Orhun Kara، نويسنده ,
Abstract :
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.