Rank 2 Totally Arithmetically Cohen-Macaulay Vector Bundles on an Abelian Surface with $Num(X) \cong \mathbb Z$

Here we classify all totally arithmetically Cohen- Macaulay rank 2 vector bundles on an abelian surface X such that $Num(X) \cong \mathbb Z$. They are the extensions of two numerically trivial, but not trivial, line bundles.