Silverman J. Advanced Topics in the Arithmetic of Elliptic Curves 1994

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In the introduction to the first volume of The Arithmetic of Elliptic Curves (Springer-Verlag, 1986), I observed that "the theory of elliptic curves is rich, varied, and amazingly vast," and as a consequence, "many important topics had to be omitted." I included a brief introduction to ten additional topics as an appendix to the first volume, with the tacit understanding that eventually there might be a second volume containing the details. You are now holding that second volume. it turned out that even those ten topics would not fit Unfortunately, into a single book, so I was forced to make some choices. The following material is covered in this book:
Elliptic and modular functions for the full modular group.
Elliptic curves with complex multiplication.
Elliptic surfaces and specialization theorems.
Neron models, Kodaira-Neron classification of special fibers, Tate's algorithm, and OGG's conductor-discriminant formula.
Tate's theory of q-curves over p-adic fields.
Neron's theory of canonical local height functions