  We study relations between some topics in number theory and supersymmetric
black holes. These relations are based on the ``attractor mechanism'' of N=2
supergravity. In IIB string compactification this mechanism singles out certain
``attractor varieties.'' We show that these attractor varieties are constructed
from products of elliptic curves with complex multiplication for N=4 and N=8
compactifications. The heterotic dual theories are related to rational
conformal field theories. In the case of N=4 theories U-duality inequivalent
backgrounds with the same horizon area are counted by the class number of a
quadratic imaginary field. The attractor varieties are defined over fields
closely related to class fields of the quadratic imaginary field. We discuss
some extensions to more general Calabi-Yau compactifications and explore
further connections to arithmetic including connections to Kronecker's
Jugendtraum and the theory of modular heights. The paper also includes a short
review of the attractor mechanism. A much shorter version of the paper
summarizing the main points is the companion note entitled ``Attractors and
Arithmetic'' (hep-th/9807056).
