curve #5744

y² = x³ − 2629901806825497876

a-invariants: [0, 0, 0, 0, -2629901806825497876]
c-invariants: [0, 2272235161097230164864]
rank (lower bound): ≥ 11
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 35563286457515224348725967345296
discriminant (Δ): -2987877677851015925715896337481180914432
Faltings height: 6.2535
naive height: 98.3501
primes of bad reduction: 2, 3, 7, 1861, 38148308389
regulator: 553162501337.348589067583014214348955340203309870781284555674
submitted by: jesper-petersen
submitted at: 2026-10-24 18:13:15 UTC
last updated: 2026-10-24 18:13:15 UTC

Witness: 11 independent points log in to add more points →

(1417773, 468973071)
(1518958, 935248006)
(7255605, 19476466443)
(9174333, 27740924631)
(13833022/9, 27014531138/27)
(268074030/169, 2563348218354/2197)
(1315315750/121, 47654068506758/1331)
(2247282622/729, 101639199133522/19683)
(12950819518/5041, 1354720834196506/357911)
(1912048659318/52441, 2643848884897489206/12008989)
(58529238351150/32041, 447774449708559213198/5735339)

Commentary

Constructed from the rational Bruin–Nasserden parametrization of the Burkhardt quartic with parameters (u,v,w)=(9/6,-9/6,-1/6) and specialization t=-1133/838. The specialization was selected through a three-stage Mestre–Nagao sieve over 328 primes. PARI/GP 2.17.4 returned matching computational rank bounds [11,11] on this model and its rationally 3-isogenous partner.

last edited by jesper-petersen at 2026-10-24 18:13:15 UTC · history