  We investigate the effect of the anisotropy of a harmonic trap on the
behaviour of a fast rotating Bose-Einstein condensate. Fast rotation is reached
when the rotational velocity is close to the smallest trapping frequency,
thereby deconfining the condensate in the corresponding direction. A striking
new feature is the non-existence of visible vortices for the ground state. The
condensate can be described with the lowest Landau level set of states, but
using distorted complex coordinates. We find that the coarse grained atomic
density behaves like an inverted parabola with large radius in the deconfined
direction, and like a fixed Gaussian in the other direction. It has no visible
vortices, but invisible vortices which are needed to recover the mixed
Thomas-Fermi Gaussian profile. There is a regime of small anisotropy and
intermediate rotational velocity where the behaviour is similar to the
isotropic case: a hexagonal Abrikosov lattice of vortices, with an inverted
parabola profile.
