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arXiv · 1203.3560

Class Numbers via 3-Isogenies and Elliptic Surfaces

Cam McLeman·Dustin Moody
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Abstract

We show that a character sum attached to a family of 3-isogenies defined on the fibers of a certain elliptic surface over $\mathbb{F}_p$ relates to the class number of the quadratic imaginary number field $\Q(\sqrt{-p})$. In this sense, this provides a higher-dimensional analog of some recent class number formulas associated to 2-isogenies of elliptic curves.

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Cam McLeman, Dustin Moody. 2012-03-15. Class Numbers via 3-Isogenies and Elliptic Surfaces. https://arxiv.org/abs/1203.3560

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