English

Class Numbers via 3-Isogenies and Elliptic Surfaces

Number Theory 2012-03-19 v1 Algebraic Geometry

Abstract

We show that a character sum attached to a family of 3-isogenies defined on the fibers of a certain elliptic surface over Fp\mathbb{F}_p relates to the class number of the quadratic imaginary number field \Q(p)\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.

Keywords

Cite

@article{arxiv.1203.3560,
  title  = {Class Numbers via 3-Isogenies and Elliptic Surfaces},
  author = {Cam McLeman and Dustin Moody},
  journal= {arXiv preprint arXiv:1203.3560},
  year   = {2012}
}

Comments

12 pages

R2 v1 2026-06-21T20:34:54.394Z