curve #4615

y² + xy = x³ − x² − 340413136509843553047095637209079x + 2376572021913322322540776527071193871425596718553

a-invariants: [1, -1, 0, -340413136509843553047095637209079, 2376572021913322322540776527071193871425596718553]
c-invariants: [16339830552472490546260590586035801, -2053358226933110413145993433263304046739057927668701]
rank (lower bound): ≥ 16
torsion subgroup: ℤ/2ℤ
conductor (N): 21357673831470329498862245870108862655389387058826297009910
discriminant (Δ): 84659937535165206608446637589190434259752585256553316251103902243580782908453975303312105045312500
Faltings height: 17.5832
naive height: 236.3367
primes of bad reduction: 2, 3, 5, 17, 31, 37, 59, 71, 79, 89, 103, 113, 181, 199, 491, 613, 797, 881, 967, 2311, 3187, 4483, 2057370727
regulator: 15473606642490040.64016690526358031468515169372648989259733581360412862
submitted by: Andrii Prokhorenkov
submitted at: 2026-10-19 03:25:08 UTC
last updated: 2026-10-19 03:25:08 UTC

(-7013778287149768, 2102171473662161259784979)
(38738985871667, 1537330420015140659139254)
(8059199225959992, 395683333575041867528629)
(8893197773954492, 229269479361504008628629)
(9418405105565192, 76782697226517604057379)
(12322149249936548, 229975081357238418966551)
(19080063345017642, 1681529742690341969547479)
(20599569160460492, 2026197312647802322010879)
(84788365039203863/4, 17315907656752427041281607/8)
(24610755179875532, 2984161178246152601127989)
(83365346246908217, 23523792353941404859430654)
(489267029047659698, 341990721894943192858404371)
(647791978009434212, 521169538299766501114893509)
(1396644288411212723/49, 1364695935033323936237070017/343)
(359725064475388687328/2209, 6780653518885405105071714596917/103823)
(131756386448043559391378/9591409, 16066337493754310124942807388018067/29704593673)

X720, T=4706/177.

last edited by Andrii Prokhorenkov at 2026-10-19 03:25:08 UTC · history