On the degree of modular parametrizations over function fields Original Research Article

Let E be an elliptic curve over Fq(T) with conductor N·∞. Let Weierstrass p : X0(N)→E be the modular parametrization by the Drinfeld modular curve of level N. Assuming that E is a strong Weil curve we prove upper and lower bounds on deg Weierstrass p. These bounds are the analogs of well-known (partially conjectural) bounds in the case of rational numbers.