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.