On Drinfeld modular curves for SL(2)

We study the Drinfeld modular curves arising from the Hecke congruence subgroups of ${\mathrm{S}\mathrm{L}}_2({\mathbb{F}}_q[T])$. Using a combinatorial method of Gekeler and Nonnengardt, we obtain a genus formula for these curves. In cases when the genus is one, we compute the Weierstrass equation of the corresponding curve.