A new canonical curve from the Mestre-Fermigier family on [348,-600,-216,492,876,-900] at the fresh shift t=2/9. Completing p6(x-t)p6(x+t) gives, after square normalization, Y^2=450555686361*x^4-8079008597280*x^3-158594291989460424*x^2+3160507498316956800*x+13015610394173754277264. Its 11 generic construction directions are enlarged by six independent points found in hyperellratpoints(Q,[1000000,2000]), with primitive-quartic sources (5618/9,140122690848), (9410/9,610042859808), (-4258/27,848258843264/9), (-33127/45,6138313886721/25), (7904/45,2379994816884/25), and (-4034/81,9044700913696/81); these map respectively to the final six displayed witnesses. The ICARM exact Cremona/Brumer verifier certifies all 17 points: F_2 rank 17, torsion rank 0, no halvings, using 18 good primes. No parity or BSD assumption is used.
Jack Cheng · 2026-08-24 07:32:42 UTC