Rank ≥16. 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)=(-7,-4), cleared tuple [-210, -120, 330, 875, -864, -11], shift t=606/1. This family satisfies the Mestre S=0 degree-drop condition identically (two depressed cubics with equal sum of squares). Certified rank 16 via 16 independent points from a quartic point search + Néron–Tate height-pairing matrix.
Seewoo Lee · 2026-06-26 06:57:26