John Coates, Minhyong Kim, Zhibin Liang, Chunlai Zhao
Published 2013-03-21, updated 2013-04-06Version 2
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.
On the $p$-part of the Birch-Swinnerton-Dyer conjecture for elliptic curves with complex multiplication by the ring of integers of $\mathbb{Q}(\sqrt{-3})$
Lower bound for the $2$-adic valuations of central $L$-values of elliptic curves with complex multiplication
Power residues of Fourier coefficients of elliptic curves with complex multiplication
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