Introduction

Modular curves in Magma are a special type CrvMod of plane curve. A modular curve X is defined in terms of standard affine modular equations which are stored in precomputed databases. Those modular curves presently available are defined by modular equations -- a bivariate polynomial relation between the j-invariant and one of several standard functions on X_0(N). These give singular, affine models for X_0(N) designed for computing isogenies of elliptic curves.