ON THE BSD CONJECTURE FOR SERIES OF ELLIPTIC CURVES WITH COMPLEX MULTIPLICATION

In the 1960’s, Birch and Swinnerton-Dyer conjectured certain relations between the group E (Q) of rational points and the L-function L_E(s) for elliptic curve E= E/Q. Suppose that E/Q is a Weil curve so that L_E(s) has a meromorphic continuation to the entire complex plane. The BSD conjecture says