I have following two questions to some steps in the proof of Prop. 5.5 (Chap. VII.5, p. 199) in Silverman's "Elliptic Curves":
At first here is the setting:
...and here the start of the proof...
The both questions are concerning the two tagged lines in the image below:
- How we conclude from the given equation $256 (1 − \lambda(1 − \lambda))^3 − j\lambda^2(1 − \lambda)2 = 0$ and the integrality of j that $\lambda$ is in $R$ ?
My ideas: we assump that $char(k) \not = 2$ ...
- Why is $j(E) \in R$ ?
Here the concerning page:
