curve #5729

y² + y = x³ + 41445099487

a-invariants: [0, 0, 1, 0, 41445099487]
c-invariants: [0, -35808565956984]
rank (lower bound): ≥ 9
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 247348263097159230659409
discriminant (Δ): -742044789291477691978227
Faltings height: 3.2592
naive height: 62.4184
primes of bad reduction: 3, 281, 589965829
regulator: 572914469533.95997800082303306365147729885001002288327432
submitted by: jesper-petersen
submitted at: 2026-10-24 17:01:19 UTC
last updated: 2026-10-24 17:01:19 UTC

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

(-41187833927/12124324, 1998381322182785/42216896168)
(-40522914431/12503296, 3803734524905537/44211654656)
(-3066622064495/1131380496, 5584012880956261543/38055114363456)
(-3011615338607/1160628624, 6122225680774859033/39540295962432)
(-1755391350383/1222621156, 8386578412666491955/42750171340696)
(13618104193/34951744, 42096741902026817/206634710528)
(163032053185/75411856, 148685868058681409/654876557504)
(42946133712913/11791353744, 383606742888107252263/1280399520353472)
(763190704269505/17372294416, 21088986244086321784319/2289737893206464)

Commentary

This curve is the 3-isogenous partner of the Mordell curve obtained from the Burkhardt rank-four family with parameters (u,v,w) = (-5,4,-2) and specialization t = -141/74. The original curve has archived matching PARI/GP rank bounds [9,9].

last edited by jesper-petersen at 2026-10-24 17:01:19 UTC · history