Suggestions for readings; Elliptic curves over function fields

Question

I would love to know some good refercences about Elliptic curves over function fields. Especially in view with Mordell-Weil's Theorem. I am already familiar with the main proof of Mordell's theorem in the book "Rational Points on Elliptic Curves" by Silverman-Tate, thus I am already familiar with the case over $\mathbb{Q}$.

Does anyone have any suggestions?

Answer 1

There are fairly detailed notes by Douglas Ulmer available online. They cover the important case of function fields over finite fields. I couldn't tell if this is the case that interest you.

Answer 2

There is Elliptic Curves: Number Theory and Criptography by Lawrence, where on chapter 8 the author treats this subject.

Answer 3

See the book "Lectures on the Mordell-Weil Theorem" of Jean-Pierre Serre.