Lemma 9.1. Assuming that:

$E ∕ K$ have integral Weierstrass equation
$y^{2} + a_{1} x y + a_{3} y = x^{3} + a_{2} x^{2} + a_{4} x + a_{6}$
$0 \neq P = (x, y) \in E (K)$

Then either

x, y \in O_{K}

{\begin{matrix} v (x) = - 2 s \\ v (y) = - 3 s \end{matrix}

for some $s \geq 1$ .