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On The Birch and Swinnerton-Dyer Conjecture for CM Elliptic Curves over $\BQ$

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arxiv 1605.01481 v1 pith:KAOJGQDZ submitted 2016-05-05 math.NT

Yongxiong Li , Yu Liu , Ye Tian This is my paper
classification math.NT
keywords birchconjectureellipticfieldswinnerton-dyeranalyticcomplexcurve
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For CM elliptic curve over rational field with analytic rank one, for any potential good ordinary prime p, not dividing the number of roots of unity in the complex multiplication field, we show the p-part of its Shafarevich-Tate group has order predicted by the Birch and Swinnerton-Dyer conjecture.

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Cited by 1 Pith paper

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  1. Explicit mock Heegner points and BSD formula on certain Mordell curves

    math.NT 2026-07 accept novelty 6.0 of 10

    Under 2 not a cube mod p, explicit mock Heegner points prove rank-1 BSD up to a 2-unit for E_{2q} and full BSD for the companion rank-0 curves E_{2q^{2}}.

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