The fusion cross section for 12 C+ 13 C has been measured down to Ec.m.=2.6 MeV at which the cross section is of the order of 20 nb. By comparing the cross sections for the three carbon isotope systems, 12 C+ 12 C, 12 C+ 13 C and 13 C+ 13 C, it is found that the cross sections for 12 C+ 13 C and 13 C+ 13 C provide an upper limit for the fusion cross section of 12 C+ 12 C over a wide energy range. After calibrating the effective nuclear potential for 12 C+ 12 C using the 12 C+ 13 C and 13 C+ 13 C fusion cross sections, it is found that a coupled-channels calculation with the Incoming Wave Boundary Condition (IWBC) is capable of predicting the major peak cross sections in 12 C+ 12 C. A qualitative explanation for this upper limit is provided by the Nogami-Imanishi model and level density differences among the compound nuclei. It is found that the strong resonance found at 2.14 MeV in 12 C+ 12 C exceeds this upper limit by a factor of more than 20. The preliminary result from the most recent measurement shows a much smaller cross section at this energy which agrees with our predicted upper limit.