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 $\bar{{\mathbb F}_q}$.

Let K be a function field with constant field k and let "infinity" be a fixed
place of K. Let C be the Dedekind domain consisting of all those elements of K
which are integral outside "infinity". The group G=GL_2(C) is important for a
number of reasons. For example, when k is finite, it plays a central role in
the theory of Drinfeld modular curves. Many properties follow from the action
of G on its associated Bruhat-Tits tree, T. Classical Bass-Serre theory shows
how a presentation for G can be derived from the structure of the quotient
graph (or fundamental domain) G\T.