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arXiv · 2610.03100

Cubic arithmetic-geometric mean and isogenies of Hesse elliptic curves

Noriyuki Otsubo
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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.

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Noriyuki Otsubo. 2026-10-02. Cubic arithmetic-geometric mean and isogenies of Hesse elliptic curves. https://arxiv.org/abs/2610.03100

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