curve #2002

y² + xy = x³ − 322187088225526568001176161794357710x + 69750098909627670414890671155413112808181411041279236

a-invariants: [1, 0, 0, -322187088225526568001176161794357710, 69750098909627670414890671155413112808181411041279236]
rank (lower bound): ≥ 16
torsion subgroup: ℤ/2ℤ
conductor (N): 24099481162217907061017365437216579033120419174904643226151662
discriminant (Δ): 38733502359472122062278265734536656424038482213154712869641500213102675354445340912141344136971481197903872
Faltings height: 19.2690
naive height: 256.8949
primes of bad reduction: 2, 3, 11, 19, 23, 47, 79, 89, 197, 241, 311, 337, 821, 827, 859, 1627, 1697, 1867, 2389, 46723, 713107
regulator: 26578852297498994132482.41527563138988052522865019627939286183521689882
submitted by: Steps Unbounded
submitted at: 2026-09-26 04:57:13 UTC
last updated: 2026-09-26 04:57:13 UTC

(26624431391330857756/25, 120836951863828605601957922714/125)
(3865098751047414433756/10201, 46871669281566997977647737317146/1030301)
(101800661642101187512096/249001, 9912234609511337584243231649011594/124251499)
(24601052674482379742332/69169, 222980143292990396861840034705998/18191447)
(659124902016439205422684/990025, 381957412989837372942548802469337558/985074875)
(617301585159764399913628/1229881, 253279256761951233642164238394509242/1363938029)
(67877096907100786012/9, 557682361690880053304250659158/27)
(3943501830708772666409212/3869089, 6807807445113892444915667693378158334/7610498063)
(16730958431263792801276/40401, 696012006189009269918637613988498/8120601)
(13557803399780565395112028/27237961, 25707345315093515656787818653099961046/142154918459)
(1764637725820863493535164/3783025, 1065207993774354357007168827371478898/7357983625)
(804221649334071795246016/231361, 712139460407375587604696106370096318/111284641)
(25623702034190471690819068/23126481, 115200676957749115247797091154502739602/111215247129)
(40886435938161243082624/46225, 6862331844921351347127961970714702/9938375)
(1263494849932018106495942656/319301161, 44472854799485698940608063810330751304682/5705592445909)
(4121169321943437123938527756/940342225, 262446184184038247687026383791395079258834/28835594329625)

2-isogenous partner of curve#1975 (Dujella (2009)).

last edited by Steps Unbounded at 2026-09-26 21:36:48 UTC · history