This paper contains a complete computation of the homotopy ring of the
spectrum of topological modular forms constructed by Hopkins and
Miller. The computation is done away from 6, and at the
(interesting) primes 2 and 3 separately, and in each of the latter
two cases, a sequence of algebraic Bockstein spectral sequences is
used to compute the E2 term of the elliptic Adams–Novikov spectral
sequence from the elliptic curve Hopf algebroid. In a further step,
all the differentials in the latter spectral sequence are
determined. The result of this computation is originally due to
Hopkins and Mahowald (unpublished).
