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PreprintarXiv licencearXiv

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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Cite

BibTeXRIS
BibTeX
@misc{otsubo2026cubic,
  title = {{Cubic arithmetic-geometric mean and isogenies of Hesse elliptic curves}},
  author = {Noriyuki Otsubo},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.03100},
  eprint = {2610.03100},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.03100},
}
RIS
TY  - UNPB
TI  - Cubic arithmetic-geometric mean and isogenies of Hesse elliptic curves
AU  - Noriyuki Otsubo
PY  - 2026
DA  - 2026/10/07
PB  - arXiv
DO  - 10.48550/arxiv.2610.03100
UR  - https://arxiv.org/abs/2610.03100
AB  - 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.
ER  -