Meromorphic c = 24 Conformal Field Theories

. Modular invariant conformal field theories with just one primary field and central charge c = 24 are considered. It has been shown previously that if the chiral algebra of such a theory contains spin-1 currents, it is either the Leech lattice CFT, or it contains a Kac-Moody sub-algebra with total central charge 24. In this paper all meromorphic modular invariant combinations of the allowed Kac-Moody combinations are obtained. The result suggests the existence of 71 meromorphic c = 24 theories, including the 41 that were already known.