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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(\sqrtp}). 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

Citation

McLeman, C. and Moody, D. (2012), Class Numbers via 3-Isogenies and Elliptic Surfaces, International Journal of Number Theory, [online], https://doi.org/10.1142/S179304211250128X, https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=911885 (Accessed May 28, 2024)

Issues

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Created November 5, 2012, Updated October 12, 2021