  We study the p-adic valuation of the values of normalised Hecke eigenforms
attached to non-isotrivial elliptic curves defined over function fields of
transcendence degree one over finite fields of characteristic p. We derive
upper bounds on the smallest attained valuation in terms of the minimal
discriminant under a certain assumption on the function field and provide
examples to show that our estimates are optimal. As an application of our
results we also prove the analogue of the degree conjecture unconditionally for
strong Weil curves with square-free conductor defined over function fields
satisfying the assumption mentioned above.
