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 December 26, 2024)
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Class Numbers via 3-Isogenies and Elliptic Surfaces
Published
Author(s)
Cam McLeman,
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
Pub Type
Journals
Download Paper
Keywords
Elliptic curve, elliptic surface, class number, character sum
Citation
Issues
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Created November 5, 2012, Updated October 12, 2021