In [1,2], we constructed motivic cycles in the group \(H^3_{{\mathcal {M}}}(A,{\mathbb {Q}}(2))\) where A is either a simple abelian surface or a product of elliptic curves. Bloch [3] constructed motivic cycles in the group \(H^3_{{\mathcal {M}}}(X_0(37)\times X_0(37))\) which generalises to hyperelliptic curves. In this paper we relate the two constructions. We show that there is a map from a hyperelliptic curve to our abelian surfaces and under that map the Bloch cycle maps to a multiple of our cycle.
