  We present an explicit momentum space computation of the four-point function
of the energy-momentum tensor in 4 spacetime dimensions for the free and
conformally invariant theory of a scalar field. The result is obtained by
explicit evaluation of the Feynman diagrams by tensor reduction. We work by
embedding the scalar field theory in a gravitational background consistently
with conformal invariance in order to derive all the terms the correlator
consists of and all the Ward identities implied by the requirements of general
covariance and anomalous Weyl symmetry. We test all these identities
numerically in several kinematic configurations. Mathematica notebooks
detailing the step-by-step computation are made publicly available through a
GitHub repository. To the best of our knowledge, this is the first explicit
result for the four-point correlation function of the energy-momentum tensor in
a conformal and non supersymmetric field theory which is readily numerically
evaluable in any kinematic configuration.
