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We compute the Adams-Novikov E_2-term of a spectrum Q(2) constructed byBehrens. The homotopy groups of Q(2) are closely tied to the 3-primary stablehomotopy groups of spheres; in particular, they are conjectured to detect thehomotopy beta family of Greek letter elements at the prime 3. Our computationleverages techniques used by Behrens to compute the rational homotopy of Q(2),and leads to a conjecture that the Adams-Novikov E_2-term for Q(2) detects thealgebraic beta family in the BP-based Adams-Novikov E_2-term for the 3-localsphere.

The Adams-Novikov E_2-term for Behrens' spectrum Q(2) at the prime 3