Birch/Swinnerton-Dyer “Notes on Elliptic Curves II”

I would like to know if any of you know if there is a more general treatment to what Birch and Swinnerton-Dyer did in "Notes on Elliptic Curves II" (http://www.ams.org/mathscinet-getitem?mr=179168).

In particular, what I am looking for is the way they were trying to compute $L(E,1)$ of an elliptic curve with complex multiplication using Hecke $L$-series. It seems to me that they were only dealing with the elliptic curve $$\Gamma_D:y^2z=x^3−Dxz^2.$$ I can't seem to find anything that talks about a general elliptic curve with CM. Any article/book related to the article is welcomed as well. Any help is appreciated, thanks!

EDIT: I would be grateful if anyone can point me to resources containing:
- Algorithms to find the Hecke Character associated to the elliptic curve.
- Computation of derivatives of $L$-series of elliptic curves with CM at $s=1$.

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There is Silverman, "Advanced topics...", chap. II, §10 and Goldstein-Schappacher, "Séries d'Eisenstein et fonctions $L$..." (Crelle, 1981) and the bibliography therein (esp. the articles of Damerell and Shimura). –  Damian Rössler Jul 24 '13 at 10:53