The greatest common valuation of φn and ψn2 at points on elliptic curves

[摘要] 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 is an element of E(K) of infinite order, we determine precisely min (v (phi(n)(P)), v (psi(2)(n)(P))), where v is a normalised valuation on K and phi(n)(P) and psi(n)(P) are polynomials arising from multiplication by n on this model of the curve. Crown Copyright (C) 2021 Published by Elsevier Inc. All rights reserved.

[发布日期] 2021-12-01

[关键词] Elliptic curves;Elliptic division polynomials;Valuations