The algebraic de Rham realization of the elliptic polylogarithm via the Poincaré bundle

In this paper, we describe the algebraic de Rham realization of the elliptic polylogarithm for arbitrary families of elliptic curves in terms of the Poincaré bundle. Our work builds on previous work of Scheider and generalizes results of Bannai-Kobayashi-Tsuji and Scheider. As an application, we compute the de Rham Eisenstein classes explicitly in terms of certain algebraic Eisenstein series.