curve #4027

y² = x³ − 121481944231254831100059915345717996900x + 514443208917775018592025382718077223635273061622553200000

a-invariants: [0, 0, 0, -121481944231254831100059915345717996900, 514443208917775018592025382718077223635273061622553200000]
c-invariants: [5831133323100231892802875936594463851200, -444478932504957616063509930668418721220875925241885964800000]
rank (lower bound): ≥ 12
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 993341250332563583452696030304878442448829037616331200
discriminant (Δ): 410503033449690779140024810381225739736406511722969674844879974202397000614807854803264254055459695730573376000000 ☆ record for ℤ/2ℤ × ℤ/2ℤ torsion, rank ≥ 12
Faltings height: 20.6862 ☆ record for ℤ/2ℤ × ℤ/2ℤ torsion, rank ≥ 12
naive height: 274.6921 ☆ record for ℤ/2ℤ × ℤ/2ℤ torsion, rank ≥ 12
primes of bad reduction: 2, 3, 5, 17, 23, 37, 43, 53, 59, 71, 151, 173, 241, 257, 691, 1033, 1039, 1667, 5323, 8219, 10723, 532241
regulator: 3810687074509.9658628188241348845652191712567357795059036422969
submitted by: dujella
submitted at: 2026-10-05 14:42:29 UTC
last updated: 2026-10-05 14:42:29 UTC

(1974944172343218930, 16799590239602262596402092200)
(-10947250676974813070, 23073639374199993606599931800)
(6017712811354714320, 1148213106968972087407145400)
(2388075972924962170, 15425760000243021533174306800)
(7089354891443062149, 3085149277932012721482239043)
(-9568569056173752855/4, 225048494633436271238403400875/8)
(6723418002353509170, 1263746900635249643043982200)
(350299584754171028349/25, 4942311722754453942687040070007/125)
(6586687242040294924, 198575644315137684520162132)
(-11781192624493600224, 17619792741635366603522257776)
(-10397897720840796930, 25562043142583394268864715400)
(5358225326671210380, 4165732621979020076708443500)

induced by the rational Diophantine triple {987007658792680/72335758720871, 243677597596104/1682226946997, 173319982599480/506350311046097 }

last edited by dujella at 2026-10-05 14:42:29 UTC · history