  We continue work of Gekeler and others on elliptic curves over ${\mathbb
F}_q(T)$ with conductor $\infty\cdot{\mathfrak n}$ where ${\mathfrak
n}\in{\mathbb F}_q[T]$ has degree 3. Because of the Frobenius isogeny there are
infinitely many curves in each isogeny class, and we discuss in particular
which of these curves is the strong Weil curve with respect to the
uniformization by the Drinfeld modular curve $X_0({\mathfrak n})$. As a
corollary we obtain that the strong Weil curve $E/{\mathbb F}_q(T)$ always
gives a rational elliptic surface over $\bar{{\mathbb F}_q}$.
