  We study holographic supersymmetric Renyi entropies from a family of
hyperbolic black holes in an Einstein-Maxwell-dilaton (EMD) system under the
BPS condition. We calculate the thermodynamic quantities of these hyperbolic
black holes. We find a remarkably simple formula of the supersymmetric Renyi
entropy that unifies (interpolates) 11 cases embeddable to 10 or 11 dimensional
supergravity. It reproduces many known results in the literature, and gives new
results with distinctive features. We show that the supersymmetric version of
the modular entropy and the capacity of entanglement cannot be mapped to
thermal quantities, due to the dependence of the temperature and the chemical
potential by the BPS condition. We also calculate the entanglement spectrum. We
derive the potential of the EMD system from a $V=0$ solution and obtain two
neutral solutions with scalar hair as a byproduct.
