curve #6226

y² = x³ − 17143450269131

a-invariants: [0, 0, 0, 0, -17143450269131]
c-invariants: [0, 14811941032529184]
rank (lower bound): ≥ 10
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 31740971810058117683801477388
discriminant (Δ): -126963887240232470735205909552
Faltings height: 4.2634
naive height: 74.4684
primes of bad reduction: 2, 3, 227, 929, 81293657
regulator: 14144489204.28145992072859530730467388913213347690525810108
submitted by: jesper-petersen
submitted at: 2026-10-31 08:48:15 UTC
last updated: 2026-10-31 08:48:15 UTC

Witness: 10 independent points log in to add more points →

(28995, 2689412)
(60483, 14286884)
(76911, 20923870)
(315499/9, 137503000/27)
(947353/36, 224462429/216)
(1416199/9, 1681623890/27)
(9751641/100, 30169255811/1000)
(13892035/81, 51690368152/729)
(17820751/225, 73920393874/3375)
(1388568105/23716, 49483843995893/3652264)

Commentary

Bruin–Nasserden rational parametrization of the Burkhardt quartic with parameters (u,v,w)=(13/9,4/9,16/9), specialized at t=-60/151. PARI/GP 2.17.4 returned rank bounds [10,10].

last edited by jesper-petersen at 2026-10-31 08:48:15 UTC · history