There is no direct ...

There is no direct relationship with conuctivity and pH, however it is the case that Conductivity is related to ionic mobility, which is higher if the ion is smaller. For example, the highest conductivity is given by H3O+. So the lower the pH, the higher the conductivity. It is also the case that  there is a conductivity minimum at neutral pH.  It seems then that your high conductivity is related to the very low pH (and hence very high concentration of H3O+ ions).