  We investigate the ramification of modular parametrizations of elliptic
curves over Q at the cusps. We prove that if the modular form associated to the
elliptic curve has minimal level among its twists by Dirichlet characters, then
the modular parametrization is unramified at the cusps. The proof uses
Bushnell's formula for the Godement-Jacquet local constant of a cuspidal
automorphic representation of GL(2). We also report on numerical computations
indicating that in general, the ramification index at a cusp seems to be a
divisor of 24.
