Elliptic Curve over ℚ Achieves Rank ≥ 29, Breaking Record — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: Elliptic curve over ℚ with rank ≥ 29 discovered, breaking previous record of 28 (Elkies 2006) | MATH: y² = x³ + ax + b with rank r ≥ 29; Mordell-Weil group E(ℚ) ≅ ℤ²⁹ ⊕ Torsion; height pairing matrix of 29 independent points; BSD conjecture predicts L⁽ʳ⁾(E,1)/r! = Ω·Reg·∏cₚ·|Ш|/|Tors|² | CONNECTION: Lattice basis of 29 independent points in Mordell-Weil lattice; regulator Reg = det(⟨Pᵢ,Pⱼ⟩) encodes geometric height pairing; no golden ratio/CM structure — generic high-rank construction via Mestre-Nagao method | DEPTH: 9 FINDING: Classification of elliptic curve configurations on Fano surface of cubic threefold | MATH: Fano surface S = F(X) of lines on cubic threefold X ⊂ ℙ Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225450283