I am a confirmed mathochist. My background is in analysis, and fairly traditional analysis at that; mainly harmonic functions, subharmonic functions and boundary behaviour of functions, but I have for many years had an interest in number theory (who hasn't?) without ever having the time to indulge this interest very much.
Having recently retired from teaching, I now do have the time, and would like to look more deeply into a branch of number theory in which my previous experience might still be useful, and in particular, I would be interested to find out more about the interplay between elliptic curves, complex multiplication, modular groups etc.
I am pretty confident in my background with respect to complex analysis, and I have a working knowledge of the basics of p-adic numbers, but my algebra background is much, much weaker: just what I can remember from courses many years ago in groups, rings, fields and Galois Theory, and absolutely no knowledge of the machinery of homolgy/cohomology, and very little of algebraic geometry (I once read the first 2-3 chapters of Fulton before getting bored and going back to analysis!)
Alas, I now no longer have easy access to a good academic library, so I would need to puchase any text(s) needed, unless any good ones happen to be available online.
My request would then be this:
What text(s) would you recommend for someone who wants to find out more about elliptic curves, complex multiplication and modular groups, bearing in mind that I am very unlikely to want to do any original research, and it is all "just for fun"?
Many thanks for your time!