Jack Morava showed that one could study the K(n)-local sphere in terms of the action of the group automorphisms of a height n formal group on its Lubin-Tate moduli space of deformations. For n = 2, one can take the height 2 formal group to be the formal completion of a supersingular elliptic curve. I will describe a piece of the K(2)-local sphere that you get from considering certain isogenies of this elliptic curve, and how it relates to the whole sphere. This approach will be compared to that of Goerss, Henn, Mahowald, and Rezk.