curve #228

y² = x³ − x² − 1054784785150680128656x + 13065457517847594395316291335056

a-invariants: [0, -1, 0, -1054784785150680128656, 13065457517847594395316291335056]
rank (lower bound): ≥ 17
conductor (N): 762280333750526640710523123060225480376357258533234759120
naive height: 156.8365
Faltings height: 10.9308
discriminant (Δ): 1360395974824539864077627986338200801298862217868752080515916800
primes of bad reduction: 2, 3, 5, 11, 13, 2673780583403, 127364387666511563, 65221931972159992355269
regulator: 7177491058583459.51584888066459172079556927610102951940280269290181167717
submitted by: Alexey Pozdnyakov
last updated: 2026-07-01 22:34:40

Witness: 17 independent points

(17260477840, -40992094518804)
(17246277940, 63064660477104)
(24225497616, -1315334066540780)
(11406892960, 1586780838736236)
(284620084, -3572851471915440)
(40638644366, -6108611231978970)
(20259905326, 107585434400730)
(15878430446, -566103220644390)
(13834761766, 1058651718838230)
(14208971316, 973020615775120)
(-25673092112, -4819098757440084)
(21213251841, -485848870950080)
(-3324637152, 4066384915623316)
(16892740438, -260467627781334)
(27534201573, -2212999545762434)
(221094522540, -102895942434903904)
(155912503597/4, 44664916210304247/8)

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, and conductor analysis. Candidate came from family mestre_u2_v5 with specialization T=4092/1.

last edited by Alexey Pozdnyakov at 2026-06-25 23:18:45 · history