  We show that the standard Hamiltonian of isotropic loop quantum cosmology is
selected by physical criteria plus one choice: that it have a `minimal' number
of terms. We also show the freedom, and boundedness of energy density, even
when this choice is relaxed. A criterion used is covariance under dilations,
the continuous diffeomorphisms remaining in this context, which are not
canonical but conformally canonical transformations. We propose how to
implement conformally canonical transformations in quantum theory. Removal of
the infrared regulator yields independence of ordering ambiguities.
