Let E be a CM-elliptic curve over ℚ with good ordinary reduction at a prime p≥5. The purpose of this paper is to construct the p-adic elliptic polylogarithm of E, following the method of A. Beĭlinson and A. Levin. Our main result is that the specializations of this object at torsion points give the special values of the one-variable p-adic L-function of the Grössencharakter associated to E.
Kenichi Bannai. "On the p-adic realization of elliptic polylogarithms for CM-elliptic curves." Duke Math. J. 113 (2) 193 - 236, 1 June 2002. https://doi.org/10.1215/S0012-7094-02-11321-0