The Eisenstein Cyclotomic Node at Level 12 in a Pell–Pythagorean Family
Year: 2025
Type: preprint
Abstract: This preprint determines the complete rational point set of the affinegenus-three curve arising from the Eisenstein norm-square condition on thePell-Pythagorean orbit generated by 2+sqrt(3). An explicit involution givesa genus-two quotient whose rational points are determined completely by acertified Magma computation. Exact lifting yields eight rational points onthe original curve and proves that the unique positive Pell index is n=2,corresponding to the primitive Pythagorean triple (33,56,65) and H_2=61^2.An independent four-cover descent and classical Chabauty verification isincluded, together with executable Magma scripts and matching output logs.The genus-two quotient used in the principal proof was identified by JohnVoight and is acknowledged in the manuscript.
Author: Méndez Ibarra, Rogelio
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7117452355
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