Not something I expected...the C1-C2 cis form is more stable than the C1-C2 trans form. Both ab initio methods and MMFF say this, and also indicate the geometry to be perfectly planar. The problem with the perfectly planar geometry is that the C4 hydrogen-carbonyl oxygen distance is short in the cis form (2.35 A) and the C4 hydrogen- sp3 ester oxygen distance is almost the same (2.39 A) in the trans. Both these distances are short. A little non planarity could preserve the conjugation, but get rid of the distances. However, both methods don't seem to be doing this. Electronics seems to overwhelm sterics.
Interestingly, a look through the Cambridge Structural Database also indicates several similar C1-C2 cis esters, with short distances (although longer than the ones above by perhaps 0.1 A or so). So this is not a purely theoretical observation.
The simple things that defy us...I am trying to figure the reasons for this one out. Maybe it's the electrostatic attraction/HB between the C4 hydrogen and carbonyl oxygen.