  Twisted bilayer graphene near the magic angle is known to have a cascade of
insulating phases at integer filling factors of the low-energy bands. In this
Letter we address the nature of these phases through an unrestricted,
large-scale Hartree-Fock calculation on the lattice that self-consistently
accounts for all electronic bands. Using numerically unbiased methods, we show
that Coulomb interactions produce ferromagnetic insulating states at integer
fillings $\nu\in[-3,3]$ with maximal spin polarization $M_{\text{FM}}=4-|\nu|$.
We find that the $\nu=0$ state is a pure ferromagnet, whereas all other
insulating states are spin-valley polarized. At odd filling factors $|\nu|=1,3$
those states have a quantum anomalous Hall effect with Chern number
$\mathcal{C}=1$. Except for the $\nu=0,-2$ states, all other integer fillings
have insulating phases with additional sublattice symmetry breaking and
antiferromagnetism in the remote bands. We map the metal-insulator transitions
of these phases as a function of the effective dielectric constant. Our results
establish the importance of large-scale lattice calculations to faithfully
determine the ground states of TBG at integer fillings.
