Isogenies of elliptic curves and the Morava stabilizer group

AbstractLet S2 be the p-primary second Morava stabilizer group, C a supersingular elliptic curve over F¯p, O the ring of endomorphisms of C, and ℓ a topological generator of Zp× (or Z2×/{±1} if p=2). We show that for p>2 the group Γ⊆O[1/ℓ]× of quasi-endomorphisms of degree a power of ℓ is dense in S2. For p=2, we show that Γ is dense in an index 2 subgroup of S2