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arXiv · 2001.07332

Elliptic curves and lower bounds for class numbers

Michael Griffin·Ken Ono
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Abstract

Ideal class pairings map the rational points of rank $r\geq 1$ elliptic curves $E/\Q$ to the ideal class groups $\CL(-D)$ of certain imaginary quadratic fields. These pairings imply that $$h(-D) \geq \frac{1}{2}(c(E)-\varepsilon)(\log D)^{\frac{r}{2}} $$ for sufficiently large discriminants $-D$ in certain families, where $c(E)$ is a natural constant. These bounds are effective, and they offer improvements to known lower bounds for many discriminants.

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Michael Griffin, Ken Ono. 2020-01-21. Elliptic curves and lower bounds for class numbers. https://arxiv.org/abs/2001.07332

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