Advanced Topics in the Arithmetic of Elliptic Curves

In The Arithmetic of Elliptic Curves, the author presented basic theory culminating in two fundamental global results, the Mordell-Weil theorem on the finite generation of the group of rational points and Siegel's theorem on the finiteness of the set of integral points. This book continues the study of elliptic curves by presenting six important, but somewhat more specialised topics: I. Elliptic and modular functions for the full modular group. Il. Elliptic curves with complex multiplication. III. Elliptic surfaces and specialisation theorems. IV. Neron models, Kodaira-N ron classification of special fibres, Tate's algorithm, and Ogg's conductor-discriminant formula. V. Tate's theory of q-curves over p-adic fields. VI. Neron's theory of canonical local height functions.