Questions tagged [birch-swinnerton-dyer]

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 ...

The vanishing part of the Beilinson-Bloch conjecture asserts that for a smooth projective variety $X$ over a number field $K$, $\dim_{\mathbb{Q}} \operatorname{CH}^i(X) \otimes_{\mathbb{Z}} \mathbb{Q} ...

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 ...

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{...