  We investigate twisted bilayer graphene near charge neutrality using a
generalized Bistritzer-MacDonald continuum model, accounting for corrugation
effects. The Fermi velocity vanishes for particular twist angles properly
reproducing the physics of the celebrated magic angles. Using group
representation theory, we identify all contact interaction potentials
compatible with the symmetries of the model. This enables us to identify two
classes of quartic interactions leading to either the opening of a gap or to
nematic ordering. We then implement a renormalization group analysis to study
the competition between these interactions for a twist angle approaching the
first magic value. This combined group theory-renormalization study reveals
that the proximity to the first magic angle favors the occurrence of a
layer-polarized, gapped state with a spatial modulation of interlayer
correlations, which we call nematic insulator.
