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Let q be a prime power and E a non-isotrivial elliptic curve over Fq(T) givenby a Weierstrass model. We survey the construction, with an explicit point ofview, of the modular parametrization of E by the associated Drinfeld modularcurve. We then prove a formula that allows us to evaluate this modularparametrization at cusps and we produce an explicit method to compute thesevalues. Finally we illustrate our results with several examples incharacteristic 2 and 3.

Explicit computation of the modular parametrization of elliptic curves over function fields by Drinfeld modular curves