In this paper, we study the cobordism spectrum M O[8] at the prime 3.
This spectrum is important because it is conjectured to play the role
for elliptic cohomology that Spin cobordism plays for real K-theory. W
e show that the torsion is all killed by 3, and that the Adams-Novikov
spectral sequence collapses after only 2 differentials. Many of our m
ethods apply more generally.