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Publication Citation: Class Numbers via 3-Isogenies and Elliptic Surfaces

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Author(s): Cam McLeman; Dustin Moody;
Title: Class Numbers via 3-Isogenies and Elliptic Surfaces
Published: November 06, 2012
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
Pages: pp. 125 - 138
Keywords: Elliptic curve; elliptic surface; class number; character sum;
Research Areas: Math
DOI: http://dx.doi.org/10.1142/S179304211250128X  (Note: May link to a non-U.S. Government webpage)
PDF version: PDF Document Click here to retrieve PDF version of paper (484KB)