In this note we prove a formula for the cancellation exponent $k_{ v,n}$ between division polynomials $\psi_n$ and $\phi_n$ associated with a sequence $\{ nP\}_{ n\in\mathbb{ N}}$ of points on an elliptic curve $E$ defined over a discrete valuation field $K$. The formula is identical with the result of Yabuta-Voutier for the case of finite extension of $\mathbb{ Q}_{ p}$ and generalizes to the case of non-standard Kodaira types for non-perfect residue fields.
Categories: math.NT math.AG