This paper is the elliptic analogue of Deligne's and Beilinson's
"Interpretation motivique..."-article in the Seattle proceedings.
We describe a general machinery giving one-extensions from formal
linear combinations of elements of the Mordell-Weil group in any
category of smooth mixed sheaves "with elliptic polylogs", a notion
which is axiomatized.
It is shown that the analogue of Zagier's conjecture is implied by the
results of "Polylogarithmic Extensions...Part III" (these archives, #69) and
the conjecture that there is a category of mixed motivic sheaves with
elliptic polylogs, and with the right Ext-groups.
This paper has been succeeded by 0134.