The greatest common valuation of ϕn and [formula omitted] at points on elliptic curves.

Given a minimal model of an elliptic curve, E / K , over a finite extension, K , of Q p for any rational prime, p , and any point P ∈ E (K) of infinite order, we determine precisely min ⁡ (v (ϕ n (P)) , v (ψ n 2 (P))) , where v is a normalised valuation on K and ϕ n (P) and ψ n (P) are polynomials arising from multiplication by n on this model of the curve. [ABSTRACT FROM AUTHOR]