curve #4629

y² + xy = x³ − 42024125089109776399490768805486967988x + 1285611293077799668355532320506749581635839193171614056592

a-invariants: [1, 0, 0, -42024125089109776399490768805486967988, 1285611293077799668355532320506749581635839193171614056592]
c-invariants: [2017158004277269267175556902663374463425, -1110768157219218913462205661924247542434128398254269606590625]
rank (lower bound): ≥ 17
torsion subgroup: ℤ/2ℤ
conductor (N): 48132758481351491535523418003114261028745289222225156169871950
discriminant (Δ): -709258235883634627380126100335376302921757255136507353170057311285344063858753825188054877015634809090474268016000000
Faltings height: 21.1012
naive height: 276.5203
primes of bad reduction: 2, 3, 5, 7, 11, 13, 37, 43, 47, 53, 67, 131, 181, 547, 673, 733, 839, 21569, 109717, 2534401, 13727437, 248323087
regulator: 204440829836447073762.806007828743746917371588701303593556305904409445554
submitted by: Andrii Prokhorenkov
submitted at: 2026-10-19 03:31:45 UTC
last updated: 2026-10-19 03:31:45 UTC

(-8762460988610391348, 31321844833414488474357967224)
(1396319473075212952, 35066431300806151504695742924)
(12215414870863808152, 50941230045373485470284530124)
(16976651088211187152, 73925412865964683459413090724)
(-92847201112271064992/9, 672948295998281039001942456988/27)
(29521136627815725952, 160538494911435403131250731124)
(47419605021347465686, 325455781729132187954092141480)
(-9204614467698390104, 29875857639718639528884990124)
(-1838381805206323598, 36832792418166503959137551224)
(3000284389445526952, 34446112200543587588928922924)
(6959267897386610662, 36471924855982858507652027944)
(38521980748964368664268/841, 7535525969634283110444449626923948/24389)
(-2042961256198235017355798387481168/5591417424159961, -15080220007786377738083052767103067209425295324389196/418102604788569352704541)
(5307270626490959331547693/3139984, 194296962179839822562209822027260542477/5564051648)
(-57271355391389306529458028/44102881, -10713402500365762767395453979216897100176/292887232721)
(8252274069423842389984/729, 935815888593471256960977741394340/19683)
(17710100429640396520758496/863041, 76333540424568875982774762924008904596/801765089)

X400, T=-5245/1466

last edited by Andrii Prokhorenkov at 2026-10-19 03:31:45 UTC · history