curve #5788

y² + y = x³ + 1347770599104

a-invariants: [0, 0, 1, 0, 1347770599104]
c-invariants: [0, -1164473797626072]
rank (lower bound): ≥ 9
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 141467779688813072909649
discriminant (Δ): -784721773933846115429823003
Faltings height: 3.8395
naive height: 69.3821
primes of bad reduction: 3, 43, 2689, 1084297
regulator: 2620594156.2836059369956310492905029687438871555353921518
submitted by: jesper-petersen
submitted at: 2026-10-25 08:39:04 UTC
last updated: 2026-10-25 08:39:04 UTC

Witness: 9 independent points log in to add more points →

(-4687/4, 9281933/8)
(-448, 1160896)
(86, 1160935)
(1032, 1161408)
(-6359907174/1207801, 1455133561573845/1327373299)
(-829502336/81225, 12307989643712/23149125)
(-41333719/4096, 148325220565/262144)
(26261584484/877969, 4361647412622592/822656953)
(123351925534/25250625, 153543150692560423/126884390625)

Commentary

The rationally 3-isogenous partner of the specialization t=-234/95 of a generic rank-four Burkhardt Mordell family with construction parameters (-9,-1,0).

last edited by jesper-petersen at 2026-10-25 08:39:04 UTC · history