  Twisted bilayer graphene (TBG) is remarkable for its topological flat bands,
which drive strongly-interacting physics at integer fillings, and its simple
theoretical description facilitated by the Bistritzer-MacDonald Hamiltonian, a
continuum model coupling two Dirac fermions. Due to the large moir\'e unit
cell, TBG offers the unprecedented opportunity to observe reentrant Hofstadter
phases in laboratory-strength magnetic fields near $25$T. This Letter is
devoted to magic angle TBG at $2\pi$ flux where the magnetic translation group
commutes. We use a newly developed gauge-invariant formalism to determine the
exact single-particle band structure and topology. We find that the
characteristic TBG flat bands reemerge at $2\pi$ flux, but, due to the magnetic
field breaking $C_{2z} \mathcal{T}$, they split and acquire Chern number
$\pm1$. We show that reentrant correlated insulating states appear at $2\pi$
flux driven by the Coulomb interaction at integer fillings, and we predict the
characteristic Landau fans from their excitation spectrum. We conjecture that
superconductivity can also be re-entrant at $2\pi$ flux.
