  Assuming that the near horizon geometry of the black hole solution of the
gravity dual to the ABJM model, in the presence of a coupling between the Weyl
tensor and the field strength, is $AdS_{2}\times S^{2}$, we compute Sen's
entropy function for this theory. By extremizing the entropy function we write
a formula for the entropy of the black hole, and then we compute the same
entropy using Wald's formula and show that the results are the same. In this
way we generalize the calculation of black hole entropy to cases of curvature
coupling to the field strength, including at first order, and we also show how
to calculate the black hole entropy when the black hole solution is unknown,
from just a few simple assumptions about the horizon.
