  In this paper, we regard dilaton in Weyl-scaled induced gravitational theory
as coupled Quintessence, which is called DCQ model by us. Parametrization of
the dark energy model is a good method by which we can construct the scalar
potential directly from the effective equation of state function
$\omega_\sigma(z)$ describing the properties of the dark energy. Applying this
method to the DCQ model, we consider four parametrizations of $\omega(z)$ and
investigate the features of the constructed DCQ potentials, which possess two
different evolutive behaviors called "O" mode and "E" mode. Lastly, we comprise
the results of the constructed DCQ model with those of quintessence model
numerically.
