The Adams–Novikov E2-term for computing π∗(L2V(0)) at the prime 2

Let V(0) denote the mod p Moore spectrum and L2 denote the Bousfield localization functor with respect to v2−1BP. The E2-term E2∗(L2V(0)) of the Adams–Novikov spectral sequence for computing homotopy groups π∗(L2V(0)) is E2∗(L2V(0))=ExtΓ∗(A,A) over the Hopf algebroid (A,Γ)=(E(2)∗,E(2)∗E(2)) for the Johnson–Wilson spectrum E(2), and obtained immediately from the chromatic E1-term H∗M11=ExtΓ∗(A,A/(v1∞)) for the generator v1 of A=Z/p[v1,v2±1]. In this paper, we determine the module structure of the E2-term E2∗(L2V(0)) at the prime 2 after determining H∗M11.