A question about the proof of Tate's algorithm in ATAEC

(I'm sorry for my English.)

Hello. I have been reading the book Advanced Topics in the Arithmetic of Elliptic Curves written by Joseph H. Silverman.

In the course of the proof of Tate's algorithm (page 375, at the end of the proof of Step 8), there is an equality on the order as follows:

$$\operatorname{ord}_{F_2'}(\tilde{\mathscr{U}}')=\operatorname{ord}_{F_2'}(\pi)=\operatorname{ord}_{F_2'}(\pi'y')=2$$

Here is my question: Why is the first part of the equality valid?

Thanks.