Let E be an elliptic curve defined over a finite extension of Q_p.

Let F_n denote the n-division polynomial of E, and let P be a K-rational point.

It is known that the sequence (F_n(P))_n forms an elliptic divisibility sequence, a subject that has been studied by many authors-among them Ward, Shipsey, and Silverman- from various perspectives.

Silverman proved that when E has good ordinary reduction, this sequence admits a p-adically convergent subsequence whose limit is algebraic if both E and P are defined over a number field.

We remove the ordinarity assumption and give an explicit description of the limit in terms of Mumford’s algebraic theta function.