Classification of three-generation models by orbifolding magnetized T2 x T2

We study orbifolding by the Z(2)((per)) permutaion of T-1(2) x T-2(2) with magnetic fluxes and its twisted orbifolds. We classify the possible three-generation models which lead to non-vanishingYukawa couplings on the magnetized T-1(2) x T-2(2) and orbifolds including the Z(2)((per)) permutation and Z(2)((t)) twist. We also study the modular symmetry on such orbifold models. As an illustrating model, we examine the realization of quark masses and mixing angles.