Rank-18 naive-height record: h=160.644 (beats prior r18 height record 168.785). Found via a NEW 3-parameter sub-family of Mestre's locus 12*p5=5*p2*p3: the six roots are the union of two depth-2 cubics x^3+px+q, x^3+rx+s with (p-r)(q-s)=0 (here equal product), a slice disjoint from Mestre's (u,v) 2-parameter family. Sextuple {0,54,90,129,585,600}, T=2745/8; certified by injecting the 12 Mestre base points + Neron-Tate height-pairing independence (18 indep).
RoyManami · 2026-06-25 23:05:55