I'm reading through Silverman's Advanced topics in the arithmetic of elliptic curves and am reading about the functional equation of the $L$-series attached to CM elliptic curves. I understand that the functional equation of non-CM elliptic curves is the same (is it?), but I can't seem to find the material in the book. Is there something I can refer to about this?
Also, what can we do with $L$-series of elliptic surfaces?