Year: 2026
Type: preprint
Abstract: We construct degree-three isogenies of Hesse elliptic curves over an arbitrary field of characteristic different from three, which correspond to a step of the cubic arithmetic-geometric mean. As an application, we describe the Serre-Tate canonical lift of an ordinary elliptic curve in characteristic three by the 3-adic cubic arithmetic-geometric mean. We also discuss the relations of the Hesse curves with complex and finite hypergeometric functions.
Source: arXiv (Cornell University)
Author: Otsubo, Noriyuki
Institution: Chiba University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220458949