  The full solution of the optimization problem giving the Gaussian capacity of
the single-mode fiducial Gaussian quantum channel is provided. Since it was
shown that the Gaussian capacity of an arbitrary (phase-sensitive or
insensitive) single-mode Gaussian quantum channel is equal to the Gaussian
capacity of this fiducial channel, the solution presented in this work can be
regarded as universal. The analytical study of this solution, below and above
the energy threshold, shows that the dependence of the Gaussian capacity on the
environment noise squeezing is not monotonic. In particular, the capacity may
have a saddle point, one or two extrema at finite squeezing, or be a
monotonically increasing function of the squeezing parameter. The exact
dependence is defined by the determinant of the noise covariance matrix and by
the transmissivity (or gain) of the fiducial Gaussian channel.
