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Class Numbers via 3-Isogenies and Elliptic Surfaces

Published

Author(s)

Cam McLeman, Dustin Moody

Abstract

We show that a character sum attached to a family of 3-isogenies defi ned on the fibers of a certain elliptic surface over Fp 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.
Citation
International Journal of Number Theory
Volume
9
Issue
1

Keywords

Elliptic curve, elliptic surface, class number, character sum
Created November 6, 2012, Updated November 10, 2018