Rank ≥17. Mestre–Fermigier construction from the integer 6-tuple a=[240, -1692, -996, 1260, 1776, -588] with shift t=1383/4: 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 17 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 16:00:40
Rank 17 curve from a Mestre-Fermigier 6-tuple specialization; tuple=[240, -1692, -996, 1260, 1776, -588], t=1383/4. Found via Nagao-Mestre sieve + quartic point search.
Seewoo Lee · 2026-06-25 16:07:30
Seewoo Lee · 2026-06-25 16:00:40