curve #4146

y² + xy = x³ − 1940873762249103201x + 1042223082811782070740185880

a-invariants: [1, 0, 0, -1940873762249103201, 1042223082811782070740185880]
c-invariants: [93161940587956953649, -900480743689122620001456030793]
rank (lower bound): ≥ 16
torsion subgroup: trivial
conductor (N): 1502320241602559108097159486275843982740063855505
discriminant (Δ): -1330657619195842691610437557576534670052270459055721175
Faltings height: 9.2818
naive height: 137.9455
primes of bad reduction: 3, 5, 197, 508399404941644368222388997047662938321510611
regulator: 6218906488580560.356877249085015685148522592020777924411595156174632000
submitted by: Andrii Prokhorenkov
submitted at: 2026-10-11 01:07:47 UTC
last updated: 2026-10-11 01:07:47 UTC

(23059868386476/20449, -49589257126460518758/2924207)
(25242526353, 4004511354265431)
(-80412504, -34608826302180)
(164424299521/225, 12689162350469161/3375)
(86533441896/25, 23648911737289116/125)
(8565789427/9, 204050251446887/27)
(603031980, 9544605430710)
(409063349487/529, -23649838229772273/12167)
(830380316, 1769634034610)
(96983673429/121, -1629538862114055/1331)
(20532856536/25, 184473477924144/125)
(-1597683021, 8056404478461)
(145936263, 27605855397441)
(1881206067/4, 122230723812423/8)
(747128424, 3030941824356)
(758703603, 2531141839056)

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