Rational Diophantine Quintuples via 2-Descent on Genus-One Quartic Curves — E8 Intelligence Research

FINDING: Rational Diophantine quintuples are equivalent to rational points on genus-one quartic curves; divisibility-by-2 criteria on these quartics govern the existence of D(q)-quintuples. | MATH: Quartic model C: y² = f₄(x), P ∈ C(ℚ); elliptic curve E = (C,P); 2-descent via the map E(ℚ)/2E(ℚ) → ℚ*/ℚ*²; D(q)-m-tuple: {a₁,...,a_m} ⊂ ℚ with aᵢaⱼ + q a square ∀ i Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-27
DOI
https://doi.org/10.5281/zenodo.23684326
Primary Topic
Algebraic Geometry and Number Theory
Type
preprint
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preprint

Rational Diophantine Quintuples via 2-Descent on Genus-One Quartic Curves — E8 Intelligence Research

Andrew Stewart Caldin
3 links
Zenodo (CERN European Organization for Nuclear Research)
Algebraic Geometry and Number Theory
preprint

Rational Diophantine Quintuples via 2-Descent on Genus-One Quartic Curves — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

FINDING: Rational Diophantine quintuples are equivalent to rational points on genus-one quartic curves; divisibility-by-2 criteria on these quartics govern the existence of D(q)-quintuples. | MATH: Quartic model C: y² = f₄(x), P ∈ C(ℚ); elliptic curve E = (C,P); 2-descent via the map E(ℚ)/2E(ℚ) → ℚ*/ℚ*²; D(q)-m-tuple: {a₁,...,a_m} ⊂ ℚ with aᵢaⱼ + q a square ∀ i Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
Algebraic Geometry and Number Theory
DOIOpen Access PDFOpenAlex
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Rational Diophantine Quintuples via 2-Descent on Genus-One Quartic Curves — E8 Intelligence Research — Andrew Stewart Caldin · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS