Rank ≥12. Mestre–Fermigier construction from the integer 6-tuple a=[348, -600, -216, 492, 876, -900] with shift t=8863/13: 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 12 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 16:04:19
Rank 12 curve from a Mestre-Fermigier 6-tuple specialization; tuple=[348, -600, -216, 492, 876, -900], t=8863/13. Found via Nagao-Mestre sieve + quartic point search.
Seewoo Lee · 2026-06-25 16:10:58
Seewoo Lee · 2026-06-25 16:04:19