  Using degree N isogenies of elliptic curves, we produce a spectrum Q(N). This
spectrum is built out of spectra related to tmf. At p=3 we show that the
K(2)-local sphere is built out of Q(2) and its K(2)-local Spanier-Whitehead
dual. This gives a conceptual reinterpretation a resolution of Goerss, Henn,
Mahowald, and Rezk.
