curve #1863

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y² = x³ + x² − 1832598158409626729618417042888952587380x + 32046899106401527358289676046769789729035006828953890929600

a-invariants: [0, 1, 0, -1832598158409626729618417042888952587380, 32046899106401527358289676046769789729035006828953890929600]
rank (lower bound): ≥ 23
torsion subgroup: trivial
conductor (N): 46482225082934057973425260842361370469980361423056825675885590800348299223349996618920
discriminant (Δ): -49769488978535063354024230862895021385054709011854306071396515590421694039728470085500518942340165831621221749500000000
Faltings height: 21.5251
naive height: 282.9522
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 19, 23, 37, 83, 113, 150100786391390262122409217400292786798788237925634670218145289853065673
regulator: 82790156734642293007177.4673146867292824978569000210389854578286575194475844457508008
submitted by: Ritik Jain
submitted at: 2026-09-25 17:15:53 UTC
last updated: 2026-09-25 17:15:53 UTC

Witness: 23 independent points log in to add more points →

(139355279555087464518260/5329, 17425594769050290882910868494672800/389017)
(65465136922062745790, -438906037293953759476244355750)
(242034850670674967346626/3025, -104913806789390213888980237815639174/166375)
(-755558653740653497428610/52441, -2828104157646524848375563035662001250/12008989)
(2579021871209177714285/4, -130692069325520292807400051834875/8)
(9249186475242492338, -126048011990724206619239629626)
(19477412578826419673330/1369, -4766120439985984587642548621617410/50653)
(110766702159728532137780, 36864963322348885004024537748514560)
(1304667278276143834308814/25, 1490216985642013932815625278294553138/125)
(-6011582776109944264539790/499849, -80854940540812501941084689313467171250/353393243)
(45067810986526105186010/1369, -4355682012252043488633753658136250/50653)
(2846943583049145219290, 151886610160780186074949029623250)
(2767401916603752767720486/97969, -1628384670263507509445888739480190290/30664297)
(-94887155241928336897366/7225, -142510761542309203698750628203973302/614125)
(14002778486375067514685/20164, -502297730191483950853306208648491875/2863288)
(42630473963505258731390/841, 6425033238227456464321301308967250/24389)
(23986091567924081540, 43474268553527674072836549000)
(218149272368567570179126810/12510369, 3249573321196707228627547259165765865650/44249175153)
(-238943086070322481, 180235324295018074802864434290)
(1017998409348447779279155880711218/45891425011041, 14943082756263225533710768062825596056535262651674/310883244172220278161)
(16680653869843568875435014500/869247289, 1609950328484469658163305824336192619087320/25628017821587)
(71425939766123919516086510526710/4969675942729, 1031991528401047207448282310066946877738986567350/11078784276579076933)
(-10088926226585019090453117404100077590/2094719484796688929, 612088988649073984165928097918472065745330378360348649250/3031718045072177768276218033)

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