Good online references for the course include Milne's and Skoruppa's lecture notes (see above). References for the theory of elliptic curves include Silverman-Tate's "Rational Points on Elliptic Curves", Knapp's "Elliptic Curves", and Silverman's "The Arithmetic of Elliptic Curves". References for the theory of heights include Hindry-Silverman's "An Introduction to Diophantine Geometry" and Serre's "Lectures on the Mordell-Weil Theorem".