  Putting emphasis on the relation between rational conformal field theory
(RCFT) and algebraic number theory, we consider a brane configuration in which
the D-brane intersection is an elliptic curve corresponding to RCFT. A new
approach to the generation structure of fermions is proposed in which the
flavor symmetry including the R-parity has its origin in the Galois group on
elliptic curves with complex multiplication (CM). We study the possible types
of the Galois group derived from the torsion points of the elliptic curve with
CM. A phenomenologically viable example of the Galois group is presented, in
which the characteristic texture of fermion masses and mixings is reproduced
and the mixed-anomaly conditions are satisfied.
