Rank ≥15. 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)=(1,-3), cleared tuple [20, -60, 40, 125, 3, -128], shift t=213. Two depressed cubics with equal product (satisfies Mestre 2e5=e2e3 identically). Certified rank 15 via 15 independent points (quartic point search + Néron–Tate height-pairing matrix). Smallest-conductor rank-15 of the family.
Seewoo Lee · 2026-06-26 15:03:44