  We report on finite-size exact-diagonalization calculations in a Hilbert
space defined by the continuum-model flat moir\'e bands of magic angle twisted
bilayer graphene (MATBG). For moir\'e band filling $3>|\nu|>2$, where
superconductivity is strongest, we obtain evidence that the ground state is a
spin ferromagnet. Near $|\nu|=3$, we find Chern insulator ground states that
have spontaneous spin, valley, and sublattice polarization, and demonstrate
that the anisotropy energy in this order-parameter space is strongly
band-filling-factor dependent. We emphasize that inclusion of the remote band
self-energy is necessary for a reliable description of MATBG flat band
correlations, and comment on possible mechanisms for superconductivity.
