curve #141

y² + xy + y = x³ − x² − 6254103958828689783047x + 192644462377949614527629133622271

a-invariants: [1, -1, 1, -6254103958828689783047, 192644462377949614527629133622271]
rank (lower bound): ≥ 16
conductor (N): 197022936627971949727076998839217404055886430 ★ record for rank ≥ 16
naive height: 162.1999
Faltings height: 11.3889
discriminant (Δ): -376536091399324797873843080279052128419264348845053873848320000000
primes of bad reduction: 2, 3, 5, 7, 13, 4957, 662481733, 3590490075461, 2040263823050317
regulator: 17919212545940.76402947779221547681853496450696895958880561434176750487
submitted by: Alexey Pozdnyakov
last updated: 2026-07-01 22:38:38

Witness: 16 independent points

(53439808611, -3322744229288306)
(-21612040989, -17824518768613106)
(186751168611, -74416602330008306)
(46440583651, -1536227171551986)
(47426885331, 1646042061718414)
(41564839011, 2121899058826894)
(46657841601, 1553506183449034)
(48467974611, -1838227029374306)
(48663260835, 1881323206446862)
(-46310678589, 19569252140718094)
(-84530314589, -10830706474635506)
(46331440071, 1529027925038974)
(52676761011, 3060719801512894)
(18056988411, -9252130297002506)
(63593508531, -7218393089868146)
(27919745211, 6308334046772494)

Commentary

Generated with assistance from OpenAI Codex, based on GPT-5. Method: generalized Mestre/Fermigier quartic-family search, sieving Mestre (u,v) families by Mestre-Nagao score, rescoring survivors, exact-height triaging the best candidates, and certifying top score/height candidates with GP famcert. This hit came from the low-denominator region 1 <= n <= 40, family mestre_um2_vm4, specialization T=6951/10. GP famcert certified rank >= 16. conductor record for rank 16: log N 101.991894 < 107.496352

last edited by Alexey Pozdnyakov at 2026-06-24 01:17:09 · history