curve #3543

y² + xy + y = x³ − 10493505123206200133394408x + 14226219483736784927902566683538388306

a-invariants: [1, 0, 1, -10493505123206200133394408, 14226219483736784927902566683538388306]
rank (lower bound): ≥ 18
torsion subgroup: trivial
conductor (N): 45702547177011393492705565836677121697499906505728730
discriminant (Δ): -13479857113095764786679529928810535319724327277010920960588456985581340087500
Faltings height: 13.3467
naive height: 184.6194
primes of bad reduction: 2, 3, 5, 7, 11, 13, 29, 43, 197, 358349, 38323148119, 451112664064940562672224179
regulator: 34347094943843491.080832917735698562792540787418552140266763664758939790923
submitted by: Matej Jurasić
submitted at: 2026-09-28 00:33:30 UTC
last updated: 2026-09-28 00:33:30 UTC

(1462024244270, -1417589944827173913)
(1897876644890, -1070921553458938158)
(965503928615, 2234890954300248267)
(-2330869335205, -5101146539665363983)
(1718835177740, 1125934622400809517)
(-45734472409195/16, -292350165676264739937/64)
(10946493089435/4, 19602949616778955611/8)
(2148781854515, -1264697884471222983)
(2886122364260, 2825103823669773942)
(-2980656233680, 4361500342721997537)
(780556202015, 2551669040297889717)
(35337831641435/49, -909668035693710853419/343)
(-3761691327805, -685858515856181463)
(-3487240431085, -2900308856791734183)
(330535079555, 3285400879828461417)
(433391503277, 3124071912366458973)
(59487981906125495/6889, 13621419049341004350164679/571787)
(20690188936652577245/9803161, 37346370740170221133451921547/30693697091)

Specialization at T = -5/22 of the rank-17 fibration of X1008 (equations as in curve#751).

last edited by Matej Jurasić at 2026-09-28 00:33:30 UTC · history