Abstract: The degree of the modular parametrization of an elliptic curve is an important invariant that is related to congruences of modular forms. In the case of an elliptic curve E over Q, the degrees of parameterizations of E by different Shimura curves are related to each other through Tamagawa numbers. We will discuss the analogous situation for elliptic curves over function fields, which admit different parameterizations by moduli of Drinfeld-Stuhler-modules.