curve #4142

y² + xy + y = x³ − x² − 481340991618424087077x + 3779536863850885467284626612701

a-invariants: [1, -1, 1, -481340991618424087077, 3779536863850885467284626612701]
c-invariants: [23104367597684356179681, -3265519850263195389544337790565329]
rank (lower bound): ≥ 17
torsion subgroup: trivial
conductor (N): 15785398237664679041126185421347937232887981824001810
discriminant (Δ): 966298733207136781392407925235896000288812598721360078643200000
Faltings height: 10.8297
naive height: 154.4829
primes of bad reduction: 2, 5, 7, 61, 5009, 231783129522713, 3184159496928366232637428740359
regulator: 1189927966341686.05330675628542333356647089832653518304416523846207920743
submitted by: Andrii Prokhorenkov
submitted at: 2026-10-11 01:07:17 UTC
last updated: 2026-10-11 01:07:17 UTC

(12897634345477440079101/821921746801, 223945017497588171215072018099026/745153433728039799)
(-7812772849, -2657675076135776)
(450723400099/25, -122580308073768492/125)
(65795121954639/54289, -22620614335075005624512/12649337)
(-280031369961/289, 10122488056570027912/4913)
(20635317999/5329, -756102651170541894432/389017)
(3320235679831/361, 2477724040510337056/6859)
(-5238316467699/1936, -191656550196427544379/85184)
(407785849926391/48841, -6319072886324573346336/10793861)
(608513736109/16, 407213516056116739/64)
(-147216457429349/6561, -962918836671621661696/531441)
(-216602174928881/12769, -3834806433357443266272/1442897)
(-193495476601/841, 48104302723172159824/24389)
(1089725102159/49, 692320650913081952/343)
(381289420263439/24649, -726006543572831644728/3869893)
(-1128408518781/49, -558521831120902048/343)
(-15191172249, -2754257808427776)

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