Questions tagged [birch-swinnerton-dyer]
Questions related to the Birch and Swinnerton-Dyer conjecture about the vanishing order and first Taylor coefficient of the L-functions of elliptic curves at the point 1.
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questions with no upvoted or accepted answers
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Rank 1 curves with prime conductor have trivial torsion. Why?
In the LMFDB database, there are 337912 elliptic curves over $\mathbb{Q}$ for which the rank is 1 and the conductor is a prime number.
All of these curves have trivial torsion group.
Is there a known ...
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Which proportion of elliptic curves over Q is proved to satisfy BSD conjecture?
In 2014, Bhargava and other authors proved that more than 66 % of all elliptic curves defined over $ \mathbb{Q} $ satisfy the Birch and Swinnerton-Dyer conjecture. Tonight I stumbled upon an article ...
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Rank and Taylor coefficient in Birch and Swinnerton–Dyer
I am trying to get a better understanding of the Birch and Swinnerton–Dyer conjecture. I have two questions
Why might one expect that the analytic rank of $L(E,s)$ is equal to the rank of $E(\mathbb{...