curve #223

y² + xy = x³ − x² − 13827291580782875260211544x + 19952277912018354390476665828916413300

a-invariants: [1, -1, 0, -13827291580782875260211544, 19952277912018354390476665828916413300]
rank (lower bound): ≥ 18
conductor (N): 461823608144041018516298274615425366200955693996006396490
naive height: 185.2960
Faltings height: 13.2974
discriminant (Δ): -2779860892166611369042972272150233658744639167770630104181815185350095802500
primes of bad reduction: 2, 3, 5, 13, 17, 23, 37, 71, 83, 210790277, 21964674471223643707048498855910313431
regulator: 6193872058172542.0698850916042087258173155583103051269994944405161556910590
submitted by: Alexey Pozdnyakov
last updated: 2026-07-01 22:32:40

Witness: 18 independent points

(1227784678841, 2196854315198111267)
(6134826146759/4, 12271431754018974331/8)
(1775940598451, 998540014077880622)
(2345352798959, 650718085190954954)
(4720531864626, -7737554084669710148)
(2058765048281, -459606069645467293)
(2652716024666, -1392590093046860308)
(1995845950091, 552619012550347142)
(4472914545539/4, 19412943032333863261/8)
(-2782573437314/9, 132816334947716409844/27)
(-4188336217449, 2095988457729532402)
(39452428375626, -246742606709672325398)
(811017706145096/361, 3267442518430273060958/6859)
(4617508820362619/2209, -44333795825549236071734/103823)
(-55963938077416/49, 2007499556130315331706/343)
(2216745075624, 440102525237020394)
(48407221607609/64, -1613127844760372797391/512)
(61640729874550751/27556, -2120352425314049635526503/4574296)

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 mestre_u4_vm1 with specialization T=20424/65. The same curve also appeared in the fixed sextuple_C model as T=10212/65.

last edited by Alexey Pozdnyakov at 2026-06-25 23:18:39 · history