We study the possibility of charge order at quarter filling and antiferromagnetism at halffilling in a tight-binding model of magic angle twisted bilayer graphene. We build on the model proposed by Kang and Vafek [1], relevant to a twist angle of 1.30 • , and add on-site and extended density-density interactions. Applying the variational cluster approximation with an exact-diagonalization impurity solver, we find that the system is indeed a correlated (Mott) insulator at fillings 1 4 , 1 2 and 3 4 . At quarter filling, we check that the most probable charge orders do not arise, for all values of the interaction tested. At half-filling, antiferromagnetism only arises if the local repulsion U is sufficiently large compared to the extended interactions, beyond what is expected from the simplest model of extended interactions.