  Attractor black holes in type II string compactifications on $K3 \times T^2$
are in correspondence with equivalence classes of binary quadratic forms. The
discriminant of the quadratic form governs the black hole entropy, and the
count of attractor black holes at a given entropy is given by a class number.
Here, we show this tantalizing relationship between attractors and arithmetic
can be generalized to a rich family, connecting black holes in supergravity and
string models with analogous equivalence classes of more general forms under
the action of arithmetic groups. Many of the physical theories involved have
played an earlier role in the study of "magical" supergravities, while their
mathematical counterparts are directly related to geometry-of-numbers examples
in the work of Bhargava et. al.
  This paper is dedicated to the memory of Peter Freund. The last section is
devoted to some of M.G's personal reminiscences of Peter Freund.
