For positive rational integers λ, we study the Hecke L-series attached to elliptic curves y2 = x3 − 2433Dλ over the quadratic field Q(√−3) and obtain various bounds of p(= 2, 3)-adic valuations of their values at s = 1 according to the cases of D and λ. In particular, for the case of even λ, we obtain a criterion of reaching the bounds of 3-adic valuations. From this, combining with the work of Coates and Wiles and Rubin, we obtain some results about the conjecture of Birch and Swinnerton-Dyer of these curves.