An upper bound for valuations of elliptic nets at primes of bad reduction

Let $E/K$ be an elliptic curve over a field defined by the short Weierstrass equation and let $\mathbf{P}=(P_1, P_2) \in E(K)^2\setminus \{(O, O), (\pm P, \pm P)\}$ be a pair of non-torsion points, where $O$ denotes the point at infinity. We give a uniform upper bound for the quantity $\min(ν(Φ_{(v_