  We theoretically examine the rotation of an atomic Bose-Einstein condensate
in an elliptical trap, both in the absence and presence of a quantized vortex.
Two methods of introducing the rotating potential are considered -
adiabatically increasing the rotation frequency at fixed ellipticity, and
adiabatically increasing the trap ellipticity at fixed rotation frequency.
Extensive simulations of the Gross-Pitaevskii equation are employed to map out
the points where the condensate becomes unstable and ultimately forms a vortex
lattice. We highlight the key features of having a quantized vortex in the
initial condensate. In particular, we find that the presence of the vortex
causes the instabilities to shift to lower or higher rotation frequencies,
depending on the direction of the vortex relative to the trap rotation.
