A book about Algebraic number theory in order to learn about elliptic curves? I am an undergraduate student and currently I am reading Atiyah-Macdonald book about Commutative Algebra which I find extremely clear and concise.
I would like to read and study "The arithmetic of elliptic curves" By Silverman, which covers an apparently interesting subject about which my university offers no courses.
As stated above, I need to build the necessary background in algebraic number theory.
Silverman's book gives as references Lang's or Shafarevich's books about the subject, which surely cover all needed but seem quite extensive.
Does also Samuel Pierre's book cover everything i need? If not, is there a shorter introduction than the two presented above?
I want to make clear a few things:

*

*During my master studies I will surely expand on the subject, that's why I am looking for an introduction as brief as possible.

*The final goal is to be able to write a thesis about elliptic curves from an algebraic-geometry viewpoint. That's why I am probably going to follow a scheme theory course next year, for which I am preparing with Atiyah's.

*It is also my understanding that some algebraic number theory would help me in Commutative Algebra, by presenting examples and motivation for the rather general theory.

*I am self-studying, so probably some books are better than others.

 A: Samuel's book is very usefull for the basics of algebraic number theory, i.e., Dedekind rings, splitting of primes, class group etc. with which you should surely be comfortable with at some point. Also because Elliptic curves gives you Dedekind rings as they coordinate rings.
Furthermore, the book builds every result needed, giving you some quite useful example in commutative algebra and theorems stated in a narrower generality than in the AM. This may be helpfull for somebody who is self studying.
Then probably for everything else you need you can either pick Serre's Local fields or Neukirch. However if your purpose is only understanding the book by Silverman, then you can avoid the chapters on Class field theory and just read the first couple of both books, which cover the construction and classification of local fields.
Class field theory is a beautiful subject, but is not needed and you may find yourself stuck in a rabbit hole.
Edit:
I forgot to mention that another book which covers the same material as Samuel is Marcus's "Number Fields". It has the advantage of having plenty of exercises.
