I am reading about the Mordell-Weil group of an elliptic curve over a number field using primarily Silverman's AEC. While the book is excellent in discussing materials prior to Chapter 8, I think that the exposition in Chapter 10 could have been better. But I don't know if there is any approachable text that discusses this topic in as much detail as Silverman does. Hence, the need to make this post.

In short, I am looking for algorithms to compute the Mordell-Weil group for elliptic curves over number fields or over just $\mathbb{Q}$.

From what I understand by skimming over Silverman and John Cremona's Algorithms for Modular Elliptic Curves book, there is $2$-descent algorithm (what Silverman and other texts like Husemoller, Knapp explain) that works when the set of rational points $E(\mathbb{Q})$ has a $2-$torsion point. And the other is 'general descent'. As far as I know, Silverman does not discuss this. But I would really like to read about it.

Could someone suggest some references for it? I know about Cremona's text (but I guess it discusses it in some special case? I'm not sure so correct me if I'm wrong) and Birch and Swinnerton-Dyer's Notes on Elliptic Curves Volume 1. Could someone tell me what are their prerequisites or are they somewhat self-contained? Also, are there any other references anyone would like to suggest?

Thank you very much.