curve #637

y² + xy = x³ − 879955475251239978538270234975x + 317815507230538177226001777675296379460090457

a-invariants: [1, 0, 0, -879955475251239978538270234975, 317815507230538177226001777675296379460090457]
rank (lower bound): ≥ 19
torsion subgroup: trivial
conductor (N): 5437422113979264942036818999717677836808408980545898415004130
discriminant (Δ): -27304765255044084326580212978678862557969980323510768854386311844624147420589684904000000
Faltings height: 15.9379
naive height: 218.4632
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 29, 37, 43, 877146319061, 23925217119677721607796938167430313027
regulator: 34060843587837799.17746545510956591633903273829499765513981674147157517297792
submitted by: 7fff-zip
submitted at: 2026-09-08 00:44:47 UTC
last updated: 2026-09-08 00:44:47 UTC

(3385756128970053062/1369, -5834706691712223372966764167/50653)
(52441303692624725322584/429276961, 129544572100598460490458291838067867/8894189354959)
(133745658591501776/49, -46338381678230836108212451/343)
(2414389029918796531150046/357852889, -3717073157931988690325300293316226071/6769503101213)
(6534211228552966/9, -211982627679000368942689/27)
(27803955283974748708046/20187049, 3760085704370998222372128997685161/90700411157)
(9073397282173982, 859834292411691279443525)
(29907859234487602872145711736/137277239272369, 18787847148137338128822492080793699911632139/1608413853192564466153)
(11172953659587119113465148201/16770269903104, -358699646969576208120096818547493540263971/68676804334236151808)
(15069055047275846/25, -316438718689545338119271/125)
(207449838871604, 12008187930545672553023)
(791310700672722734/841, -438233457063955846578462023/24389)
(3627765659907998476/7569, 1634775910104132392813135969/658503)
(2172379093153331/4, 2569243077159156522139/8)
(106145865329976149280157461254/210623076353881, 4682491394290157966823875370065951924430727/3056743009270109055779)
(1622549800626721841/1600, -1385031358637381673385944259/64000)
(538767181309504, -335211592795465112027)
(539648094095054, -324908580973440303427)
(4845298154112136/9, 9207380235850456463671/27)

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