Let $E$ be an elliptic curve in $\mathbb P^2$ and $p$ be any point on $E$. From $p$ we can draw four tangent lines to $E$ and let $\lambda$ be the cross ratio of their slopes. How can we prove that $\lambda$ is independent of $p$?
I saw this in a note on elliptic curves which suggests that from above we can see the j-invariant is really a invariant.
Thanks in advance.