  We compute the $\mathbb{C}$-motivic Adams spectral sequence for
$\mathit{mmf}/\tau$. Up to reindexing, this spectral sequence is isomorphic to
the algebraic Novikov spectral sequence for topological modular forms. We give
a full analysis of the inclusion and projection maps which occur in the long
exact sequence induced by multiplication by $\tau$ on Adams $E_2$-pages. Our
computation is totally algebraic and can be used to obtain the $E_2$-page of
the Adams-Novikov spectral sequence for topological modular forms in a way that
is independent from previous computations using the elliptic curves Hopf
algebroid.
