We construct ramified families of curves to explicitly model the Lubin-Tate action, the action of a formal group law on its deformation space, for a maximal finite subgroup G. We will see that as a G-representation, this deformation space is a quotient of a regular representation of a finite cyclic group! This allows us to partially compute the E2 page of the homotopy fixed point spectral sequence of the K(h, p) - local homotopy groups of spheres for height h=p^{k-1}(p-1), for all such h and p simultaneously. Thus, we resolve a 40 year old computational stalemate.