The motivic quasi-isomorphism conjecture for the elliptic Bloch complex

Let $E$ be an elliptic curve over a field $k$, let $B(E,3)$ denote the elliptic Bloch complex, and let ${\cal M}{\cal M}_k$ be the hypothetical abelian category of mixed motivic sheaves over $k$. Set ${\cal H}:=h^1(E)(1)$. Motivic quasi-isomorphism conjecture. There exists a canonical quasiisomorphism in the derived category

$$B(E,3) \otimes \Bbb Q= RHom_{{\cal M}{\cal M}_k}(\Bbb Q(0), {\cal H}(1)).$$

This is the motivic refinement of the paper's results on the elliptic Bloch complex and its relation to motivic cohomology. It is formulated in terms of a hypothetical category of mixed motivic sheaves, so its status remains open.