  New local and global non-abelian zeta functions for elliptic curves are
studied using certain refined Brill-Noether loci in moduli spaces of
semi-stable bundles. Examples of these zeta functions and a justification of
using only semi-stable bundles are given too. We end this paper with an
appendix on the so-called Weierstrass Groups for general curves, which is
motivated by a construction of Euler systems from torsion points (of elliptic
curves).
