Hi. I don't know how to make a comment; this is on Torsten's example with 
elliptic curve minus zero point. When you take a line bundle corresponding to 
a point (not a two torsion point) and add the line bundle corresponding to minus of that point then this rang=2 vector bundle restricted to the elliptic curve minus zero is 
(even globally) free. 

Indeed, working on the elliptic curve twist with the degree one line bundle L
corresponding to the zero point and take the canonical inclusion of the structure
sheaf on both factors, the quotient must be isomorphic to L squared. 

This is just to understand Bass' theorem on this nice example. I don't really understand what happens with the two torsion points.