  The coexistence curve and molecule number density of a 4-dimensional AdS
topological charged black hole in massive gravity is investigated. We find that
the analytic expression of the coexistence curve in the reduced parameter space
is dependent on theory parameters. This is very different from the previous
results obtained in other modified gravity such as $f(R)$ gravity and
Gauss-Bonnet gravity. Besides, we derive the explicit expression of the
physical quantity which describes the difference of the number densities of AdS
topological charged black hole molecules between the small and large black
hole. It is observed that the difference of the molecule number densities is
also dependent on theory parameters. Both the expressions of the coexistence
curve and the difference of the molecule number densities can be reduced into a
form which is similar to a RN-AdS black hole if the mass of graviton $m$ is
zero. Moreover, we find the shifted temperature under massive gravity. This can
highlight the important role played by the mass of graviton and other
parameters in the phase transitions of AdS black holes in massive gravity.
