curve #226

y² + xy = x³ − 53324817965388276805370879748910x + 152600569230942786227963554343099291511940660100

a-invariants: [1, 0, 0, -53324817965388276805370879748910, 152600569230942786227963554343099291511940660100]
rank (lower bound): ≥ 20
conductor (N): 282182911611488014589765703157855796043317619561544915217487973922307930
naive height: 230.8115
Faltings height: 17.1249
discriminant (Δ): -355568117955757642974912655755100242442938536081550074372306129807997878195940027796106400000000
primes of bad reduction: 2, 3, 5, 7, 31, 41, 59, 79, 1615673, 140389069210932330034578246587156827594757780759118714191
regulator: 22741880954418501814.3623903478549341506058195963051390323906246906003515483700
submitted by: Alexey Pozdnyakov
last updated: 2026-07-01 22:29:42

Witness: 20 independent points

(618601125946370, 346194302434275472478840)
(4274187758343020, 52574304621988571796290)
(1237465552904420, -297502775169095344544710)
(2942610078779420, -145486591821952222859710)
(-7399759529700580, 376838035640579185200290)
(4573716239571920, -66219377082644347492210)
(10682154885034220, -895489011065482379902510)
(5722894198425740, -186713018618338452812110)
(2302662274779020, -204989810208697277535310)
(-6015123623406730, -505686134502279456010810)
(-913586879332288, 447833570226927052727006)
(3467158396446920, -96924402816950500267210)
(-2962025209897180, 533443925142244344432890)
(-1020997989620680, 453851050081375324404290)
(6555760311182919080/2209, -14859538369702735477983935330/103823)
(35422287391675744/9, 1640631393230902228935254/27)
(1647630816630975820/361, -449530896105195331951787690/6859)
(479223846427162851980/113569, 1996522496958091344388813918370/38272753)
(417628515448521851180/94249, 1666221552406370616415079717270/28934443)
(80652470616459665420/351649, 78130442711385740206728677920930/208527857)

Commentary

Generated with assistance from OpenAI Codex, based on GPT-5. Method: Generalized Mestre/Fermigier quartic-family search: Mestre-Nagao stage sieve, high-M rescore, exact-height triage, conductor analysis, and GP famcert certification. Candidate came from family sextuple_C_m138_138_162_m60_m90_m12 with specialization T=10167/350.

last edited by Alexey Pozdnyakov at 2026-06-25 23:18:43 · history