# 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 polynomials which are stored in precomputed databases. Those modular curves presently available are defined by bivariate polynomials relating the $j$-invariant and one of several standard functions on $X_0(N)$. These give singular models for $X_0(N)$ designed for computing isogenies of elliptic curves.