  Let $A_1$ be any spectrum in the class of finite spectra whose mod-2
cohomology is isomorphic to $\mathcal{A}(1)$ as a module over the subalgebra
$\mathcal{A}(1)$ of the Steenrod algebra; let $tmf$ be the connective spectrum
of topological modular forms. In this paper, we prove that the $tmf$-Hurewicz
image of $A_1$ is surjective.
