On the 2-part of the Birch-Swinnerton-Dyer conjecture for elliptic curves with complex multiplication - Coates, J; Kim, M; Liang, Z; Zhao, C (Mathematical Institutes of the Universität Münster, 2013)
Given an elliptic curve E over Q with complex multiplication having good reduction at 2, we investigate the 2-adic valuation of the algebraic part of the L-value at 1 for a family of quadratic twists. In particular, we prove a lower bound for this valuation in terms of the Tamagawa number in a form predicted by the conjecture of Birch and Swinnerton-Dyer.