curve #3833

y² = x³ − 2084062841114420077291440492199756819407x + 36586509997281757324741595347578511283836293325100072172594

a-invariants: [0, 0, 0, -2084062841114420077291440492199756819407, 36586509997281757324741595347578511283836293325100072172594]
rank (lower bound): ≥ 24
torsion subgroup: trivial
conductor (N): 148934614245717393460171811725493421089542990615584067843263511846377514693342558938360
discriminant (Δ): 1048427398619624870796003020927629071297519349667369993571014692733716367583842738328157952977174253570075887255200000
Faltings height: 21.3714
naive height: 283.2190
primes of bad reduction: 2, 3, 5, 7, 11, 17, 23, 29, 31, 43, 47, 83, 103, 2551, 12073, 368142902891, 78026521753470397273714496936059241789678475464231
regulator: 485455972233555991226879.52570468603178337657227822633853168884700872363292679133693555
submitted by: 7fff-zip
submitted at: 2026-10-03 05:22:32 UTC
last updated: 2026-10-03 05:22:32 UTC

Witness: 24 independent points log in to add more points →

(1079430256711862993943/121, 182034482734318281706579701355560/1331)
(5685651360673954384497/169, 148214328645683346616502955221850/2197)
(13244762362621620803433/21316, 584649442398335944364588789324012925/3112136)
(29015803946475961233, -23337657933202901457936014490)
(-1226087806051955180109/25, 18042300287851940996473359801936/125)
(-46059236435370126207, 186719939500109290599994064010)
(557034298795190464407297/1024, -414321875887279435543321247223200385/32768)
(102186177450756854577/4, 34169849973485034201862952175/8)
(1469037234049445136618, -56278422015794198386885124545590)
(29387711413014464073, -26851530385705437053723211570)
(4081954726086050334337/1024, 5516538074010450779148941831552575/32768)
(-101263209445210646897967/5041, -94927437084064165661988648641057850/357911)
(-92232289833310707383/9, -6438681037826373153926580575950/27)
(10697697977223928239057/64, -1068889348934507677772475472448025/512)
(4654429315022040259047/169, 19572810050436485636350867325400/2197)
(52520408077728015382/9, -4236804860628476795557626999260/27)
(-79733333112172711927853/11449, 276009042371518680439184637360844960/1225043)
(25504845749689651953, 4861928078248605261715617030)
(24415483570500091633, -16048812682303892752693782790)
(4321434552244850514387/169, -8579568525234625707043843649160/2197)
(6719576772451374835002/169, 282903495695331385946809842731970/2197)
(27529114137911433963, -8780878569496768243100776800)
(94167792787627798977/4, -191182820503252485954849038775/8)
(-8109865494456056339795/729, -4756375948278304981399472837420734/19683)

Commentary

X1008; T=685/43; 2-neighbor step: yes (Q has vector q=[0,2,-1,1,-1,1,2,-1,1,0,2,-2,1,1,0,1,1] in source section basis; h(Q)=12).

last edited by 7fff-zip at 2026-10-03 05:22:32 UTC · history