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arXiv · 1303.5218

On the 2-part of the Birch-Swinnerton-Dyer conjecture for elliptic curves with complex multiplication

John Coates·Minhyong Kim·Zhibin Liang·Chunlai Zhao
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Abstract

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.

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John Coates, Minhyong Kim, Zhibin Liang, Chunlai Zhao. 2013-03-21. On the 2-part of the Birch-Swinnerton-Dyer conjecture for elliptic curves with complex multiplication. https://arxiv.org/abs/1303.5218

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