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A majority of elliptic curves over $\mathbb Q$ satisfy the Birch and Swinnerton-Dyer conjecture

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arxiv 1407.1826 v2 pith:MOS2NFHS submitted 2014-07-07 math.NT

Manjul Bhargava , Christopher Skinner , Wei Zhang This is my paper
classification math.NT
keywords birchconjecturecurvesellipticmajoritymathbbsatisfyswinnerton-dyer
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abstract

We prove that a majority (in fact, $>66\%$) of all elliptic curves over $\mathbb Q$, when ordered by height, satisfy the Birch and Swinnerton-Dyer rank conjecture.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Geometry-of-numbers methods over global fields II: Coregular representations

    math.NT 2026-04 unverdicted novelty 7.0 of 10

    Geometry-of-numbers methods are extended to count orbits in coregular spaces over arbitrary global fields, yielding bounds on average ranks and Selmer sizes for elliptic curves and hyperelliptic Jacobians.

  2. On the Identification of Elliptic Curves That Admit Infinitely Many Twists Satisfying the Birch-Swinnerton-Dyer Conjecture

    math.NT 2026-01 conditional novelty 6.0 of 10

    An algorithmic scan of the LMFDB identifies 36,687 elliptic curves of conductor below 500,000 that each have infinitely many quadratic twists satisfying the full BSD conjecture, and finds a positive bias in the order ...

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