Analogy between elliptic curves and number fields

Question

The first section of this article describes a deep analogy between elliptic curves and number fields. In particular, there is the analogy between the Tate-Shafarevich group for an elliptic curve and the ideal class group of a number field. Presumably, this particular analogy is due to the fact that both arise in similar cohomological circumstances, as discussed in this paper. Are there any other books, papers, or sources that describe this analogy and prove, as in the second paper, that the "Tate-Shafarevich group" of a number field is indeed the ideal class group?

Answer 1

This was, in fact, the topic of an REU paper I wrote last year, which can be found here!