Hard ellipses in a two-dimensional setup and at high packing fractions show an intricate variety of possible lattice conformations [1]. These structures all emerge from a hexagonal arrangement of discs via suitable deformations along a chosen axis. We characterize the resulting lattice types by two parameters, namely ω and τ, which specify orientational and positional order of the particles. We show that for ellipses with aspect ratio κ = 2 only two relevant lattice types survive within the plethora of possible ordered configurations. Our simulation-based investigations rely on lattice-switch Monte Carlo moves, so that the underlying parameter space of lattice configurations is directly probed. By investigating the entropic landscape we find that ordered lattice types characterized either by ω = 0◦ - named the diagonal lattice state - or ω = 30◦ - named the parallel lattice state - are the most stable ones. In an effort to find the true ground state, i.e. the global entropy-maximum, the exact entropic difference between the parallel and diagonal state is computed. We achieve this with the help of complementary computational methods, such as a Potential Mean Force Method in combination with the Reweighting Histogram Technique [2] as well as the Einstein Crystal Method [3]. Our results show that the diagonal lattice-state is entropically favoured over the parallel one for systems sizes of up to sizes of approximately 400 particles. We find evidence that this entropic difference persists also in the thermodynamic limit. References [1]J. Vieillard‐Baron, The Journal of Chemical Physics, 56, 4729-4744 (1972) [2]G. Torrie, J. Valleau, Journal of Computational Physics, 23, 187-199 (1977) [3]C. Vega, E. Noya, The Journal of Chemical Physics, 127, 154113 (2007)