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Consider elliptic curves $ E:\ y^{2} = x^{3} + D^{3} $ defined over thequadratic field $\ \Q(\sqrt{-3}) $. Hecke $ L-$series attached to $ E $ arestudied, formulae for their values at $ s=1, $ and bound of 3-adic valuationsof these values are given. These results are complementary to those in [Q] and[QZ], and are consistent with the predictions of the conjecture of Birch andSwinnerton-Dyer.

A note on $ L(1) $ of Hecke $ L-$series associated to the elliptic curves with CM by $ \sqrt{-3} $