Let E be an elliptic curve over Q with complex multiplication by K and p be an odd prime such that E has potentially good reduction at p.In this paper,we prove that if L(s,E)has a simple zero at s=1,then the p-part of the Birch-Swinnerton-Dyer conjecture of E holds.Moreover,we give a family of elliptic curves with rank one whose conductors can be divided by any number of primes,satisfying the full Birch-Swinnerton-Dyer conjecture.
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