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 X0(N). These give singular models for X0(N) designed for computing isogenies of elliptic curves.