curve #4622

y² + xy + y = x³ − 83224674972141613037161390226510448x + 92954984218955671726136120804653137954800845166161006

a-invariants: [1, 0, 1, -83224674972141613037161390226510448, 92954984218955671726136120804653137954800845166161006]
c-invariants: [3994784398662797425783746730872501481, -80313106365177700377373784973214507331623550319871861621]
rank (lower bound): ≥ 17
torsion subgroup: ℤ/2ℤ
conductor (N): 2284850412066332199034027332367937146859263362365044317615667290
discriminant (Δ): -3695859419328959637264136339653721276780927937270275232162930559299262984833249247055298191069490925010710000
Faltings height: 19.5121
naive height: 257.4511
primes of bad reduction: 2, 3, 5, 7, 11, 19, 37, 47, 53, 79, 103, 191, 263, 461, 1759, 9613, 70881409, 370175059, 2410702669, 2802557011
regulator: 909352688525168931865.651549040197765292545143878620609496894669060822217
submitted by: Andrii Prokhorenkov
submitted at: 2026-10-19 03:30:43 UTC
last updated: 2026-10-19 03:30:43 UTC

(-23184193547496508644271/46225, 917864853738434624044498036405737/9938375)
(-464918927166625855, 176509678642609888757454927)
(50299913418144005, 298154411552853093581510667)
(89596861219626266, 293628271938985909662419094)
(153469424393335745, 289477435608453487438684527)
(200613979500831941, 290401196409245483499223599)
(-9535958869238951611/25, -32882986303904939159026142097/125)
(-94092893986646863, 316153105156141229687730519)
(7078418654535972205/9, 19357280808254104319274490229/27)
(49557848118452724125005/24649, 10981771394642906248563025699641611/3869893)
(380801656658308690, 341295913818476618838047207)
(1511621882557816645, 1849650730616908722198122927)
(3943887575274553165/9, 10125308087944480294653278549/27)
(19191966935637398980/81, -214451793581873136634508105807/729)
(54396866419723776410/841, 7228469992914517944881219203278/24389)
(17255605583565041840598605/23222761, 74348122468223274527914277989284803193/111910485259)
(5398319680523785498505/26569, 1258401667151871673327909911704469/4330747)

X400, T=-4766/1315

last edited by Andrii Prokhorenkov at 2026-10-19 03:30:43 UTC · history