Abstract

Given a minimal model of an elliptic curve, E/K, over a finite extension, K, of Qp for any rational prime, p, and any point P∈E(K) of infinite order, we determine precisely min⁡(v(ϕn(P)),v(ψn2(P))), where v is a normalised valuation on K and ϕn(P) and ψn(P) are polynomials arising from multiplication by n on this model of the curve.

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