Isogenies of elliptic curves and the Morava stabilizer group

Let S2S2 be the pp-primary second Morava stabilizer group, CC a supersingular elliptic curve over F¯p, OO the ring of endomorphisms of CC, and ℓℓ a topological generator of Zp× (or Z2×/{±1} if p=2p=2). We show that for p>2p>2 the group Γ⊆O[1/ℓ]×Γ⊆O[1/ℓ]× of quasi-endomorphisms of degree a power of ℓℓ is dense in S2S2. For p=2p=2, we show that ΓΓ is dense in an index 2 subgroup of S2S2.