2-Descent on Quartic Elliptic Curves for Rational Diophantine D(q)-Quintuples — E8 Intelligence Research

FINDING: Divisibility-by-2 descent on quartic models of elliptic curves is the operative tool for constructing rational Diophantine D(q)-quintuples — the core result is a 2-descent/2-cover machinery, not a harmonic-ratio phenomenon. | MATH: Elliptic curve in quartic (Jacobian) form: y² = f₄(x), f₄ quartic with distinct roots; 2-descent via the Kummer map E(Q)/2E(Q) ↪ Sel₂(E/Q); D(q)-m-tuple condition: for a set {a₁,…,a_m}, require aᵢaⱼ + q = □ for all i Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com