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Let $//$ denote the Hopf algebra quotient. We know that: $$HF_{2}^*(ko) \simeq A//A(1)$$ $$HF_2^*(tmf) \simeq A//A(2)$$ By Hopf invariant one, we know there is no $X$ such that $HF_2^*(X) \simeq A//...