Rank ≥15. Mestre–Fermigier construction from the integer 6-tuple a=[-138, 138, 162, -60, -90, -12] with shift t=1265/9: let p6(x)=∏(x−a_i) and q(x)=p6(x−t)·p6(x+t); completing q to g(x)²−r(x) gives the genus-1 quartic model y²=r(x), whose x=a_i±t base points plus a few small-x extra points supply 15 independent rational points. The shift t was selected by a Nagao–Mestre prime-sum sieve; the witness points were found by an integer quartic-point search and certified independent via the Néron–Tate height-pairing matrix.
Seewoo Lee · 2026-06-25 16:03:08
Rank 15 curve from a Mestre-Fermigier 6-tuple specialization; tuple=[-138, 138, 162, -60, -90, -12], t=1265/9. Found via Nagao-Mestre sieve + quartic point search.
Seewoo Lee · 2026-06-25 16:09:50
Seewoo Lee · 2026-06-25 16:03:08