Rank ≥14. Mestre construction from the rational 6-tuple family a(u,v) = {u, v, -u-v, -u(u+2v)²/((u-v)(2u+v)), v(2u+v)²/((u-v)(u+2v)), (u-v)²(u+v)/((u+2v)(2u+v))} at (u,v)=(-12,-3), giving a=(-12,-3,15,16,-27/2,-5/2) with shift t=-1161/88 (cleared: tuple (-24,-6,30,32,-27,-5), t=-1161/44). This family satisfies the Mestre S=0 degree-drop condition identically — it is a union of two depressed cubics with equal sum of squares. Certified rank 14 via 14 independent points from an integer quartic-point search + Néron–Tate height-pairing matrix.
Seewoo Lee · 2026-06-25 21:12:06