The main purpose of this paper is the geometric construction, and the analysis
of the formalism of elliptic Bloch groups. In the setting of absolute
cohomology, we obtain a generalization of Beilinson's Eisenstein symbol to
divisors of an elliptic curve, whose support is not necessarily torsion.
For motivic cohomology, such a generalization is obtained in low degrees.
Our main result shows that the Eisenstein symbol can be defined in all degrees
if the elliptic analogue of the Beilinson-Soule vanishing conjecture holds.
This paper is the final version of #213. The main improvement is that
the main results no longer require an injectivity statement on the
(product of the) regulators.