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CLASS NUMBERS VIA 3-ISOGENIES AND ELLIPTIC SURFACES

CAM McLEMAN

Department of Mathematics, University of Michigan-Flint, Flint, MI 42439, USA

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and

DUSTIN MOODY

National Institute of Standards and Technology (NIST), 100 Bureau Drive, Gaithersburg, MD, 20899, USA

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https://doi.org/10.1142/S179304211250128XCited by:0 (Source: Crossref)

Abstract

We show that a character sum attached to a family of 3-isogenies defined on the fibers of a certain elliptic surface over 𝔽_p relates to the class number of the quadratic imaginary number field . In this sense, this provides a higher-dimensional analog of some recent class number formulas associated to 2-isogenies of elliptic curves.

Keywords:

AMSC: 11T24, 14J27, 11R29

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