### A Candidate for the abelian category of mixed elliptic motives, by Owen Patashnick

In this paper we suggest a definition for the category of mixed motives
generated by the motive h^{1}(E) for E an elliptic curve without
complex multiplication. We then compute the cohomology of this category.
Modulo a strengthening of the Beilinson-Soule conjecture, we show that the
cohomology of our category agrees with the expected motivic cohomology groups.
Finally for each pure motive (Sym^{n}h^{1}(E))(-1) we construct
families of nontrivial motives whose highest associated weight graded piece is
(Sym ^{n}h^{1}(E))(-1).

This paper was essentially written in the late 1990's whilst the author was at
the University of Chicago. The author apologizes for the tardiness of this
posting, and hopes the reader will still find the content interesting.

Owen Patashnick <o.patashnick@bristol.ac.uk>