  Twisted bilayer graphene (TBG) develops large moir\'e patterns at small twist
angles with flat energy bands hosting domes of superconductivity. The large
system size and intricate band structure have however hampered investigations
into the superconducting state. Here, using full-scale atomistic modelling with
local electronic interactions, we find at and above experimentally relevant
temperatures a highly inhomogeneous superconducting state with nematic ordering
on both atomic and moir\'e length scales. The nematic state has a locally
anisotropic real-valued d-wave pairing, with a nematic vector winding
throughout the moir\'e pattern, and is three-fold degenerate. Although d-wave
symmetric, the superconducting state has a full energy gap, which we tie to a
{\pi}-phase interlayer coupling. The superconducting nematicity is further
directly detectable in the local density of states. Our results show that
atomistic modeling is essential and also that very similar local interactions
produce very different superconducting states in TBG and the high-temperature
cuprate superconductors.
