curve #6209

y² + xy = x³ − x² − 782010866890036870x + 284634123211962545221172296

a-invariants: [1, -1, 0, -782010866890036870, 284634123211962545221172296]
c-invariants: [37536521610721769769, -245923882286221291822844899797]
rank (lower bound): ≥ 17
torsion subgroup: trivial
conductor (N): 23117553694948887685408031549626710984141662473384430
discriminant (Δ): -4392335202040288660227525994429075086986915869943041700
Faltings height: 9.2305
naive height: 135.3496
primes of bad reduction: 2, 5, 19, 121671335236573093081094902892772163074429802491497
regulator: 2368858336763056.03646792137523882976991167588492916365390693020695387925
submitted by: Andrii Prokhorenkov
submitted at: 2026-10-30 17:20:02 UTC
last updated: 2026-10-30 17:20:02 UTC

(-10474279729177/10201, -2315678905658178444/1030301)
(-525946658, 23461780823390)
(127031592199794/588289, -5061734665917284841214/451217663)
(14785380355, 1794683926560549)
(148945580582/49, 55300033108911508/343)
(233615118238, -112914251311549474)
(243006841873/64, 116816642007188541/512)
(274029298294/25, 142995598891950012/125)
(353369640999133/1646089, -23767776760956750786234/2111932187)
(39375663203/4, -7783050169530475/8)
(428497767805/2209, -1229512917198037433/103823)
(432384251955635/1385329, -13735581148780198996872/1630532233)
(4807675863255856063/11349493156, 6553857290818347978355596009/1209106903881304)
(67970910, 15224753750084)
(7094736649/25, 1156236155831158/125)
(8288322330471/16900, 9593923153834769179/2197000)
(865987977, 16026324639793)

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