curve #621

y² + xy + y = x³ + x² − 31443135315521062331781565391832066x + 2146031392816454648277209082403076306227929383970063

a-invariants: [1, 1, 1, -31443135315521062331781565391832066, 2146031392816454648277209082403076306227929383970063]
rank (lower bound): ≥ 20
torsion subgroup: trivial
conductor (N): 111372581738293442499558893391879756098105496180829380581316303097386743130
discriminant (Δ): 7421000872632507202269928506373016419465561067870126880443590299229921216603476987851214034462310400
Faltings height: 18.4105
naive height: 249.9141
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 23, 41, 43, 138711007231, 38786711512304563387726708936539775997732816845590977
regulator: 55166037417134701080.4524975637987870333251978542632897918288100046702162674066
submitted by: 7fff-zip
submitted at: 2026-09-06 22:51:47 UTC
last updated: 2026-09-06 22:51:47 UTC

(178849483668406009, -47363762163315067766872957)
(-5152907815456913391/64, 33005991211168971821133385723/512)
(-4284084762779233359/121, 75467972124899621974823062809/1331)
(-18101806160357351, 52050719668304178380179427)
(-68743120157290920319/361, 240410172961047605304210958401/6859)
(100989864722616529, -764376971636931265395613)
(4624792875725085785453831/45225625, 3920909798323469889263740704037221/304142328125)
(7490610995669510189306001/72982849, 80084267903625351203697000699646461/623492479007)
(4196491360985895821992879/40921609, 18779709406891223751436420262628917/261775532773)
(66914090281210884365162289/652649209, 898366216601337913623310369504462297/16673229342323)
(16887035040603503546501049098620929/96833274329285209, 1336191538378223888512744461568940345750081015495383/30132622171260242502819677)
(600511404378363406520869/5678689, -25406903668664264240900979489062407/13532315887)
(60595825774305481, -21522260014520145412963261)
(-166936208684543853111359/1320201, -97131715285322202705494129034714449/1516910949)
(3096519910262200276129/29929, -3102232772021651749446820400417/5177717)
(70253378529747709, -16845862082825558898842557)
(59447454670330554507662745961/583000967025, -96808173459120191940171589608841537863269/445147473367103625)
(3185222574187621517/16, -3932811825187916230053882519/64)
(1682382250439768229/16, -98675062217847252995752993/64)
(1155559304108642687963/11236, -299402461420388135390266289427/1191016)

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