  Networks of coupled parametric resonators (parametrons) hold promise for
parallel computing architectures. En route to realizing complex networks, we
report an experimental and theoretical analysis of two coupled parametrons. In
contrast to previous studies, we explore the case of strong bilinear coupling
between the parametrons, as well as the role of detuning. We show that the
system can still operate as an Ising machine in this regime, even though
careful calibration is necessary to ensure that the correct solution space is
available. Apart from the formation of split normal modes, new states of mixed
symmetry are generated. Furthermore, we predict that systems with $N>2$
parametrons will undergo multiple phase transitions before arriving at a regime
that can be equivalent to the Ising problem.
