curve #4750

y² = x³ − 5721469548799

a-invariants: [0, 0, 0, 0, -5721469548799]
c-invariants: [0, 4943349690162336]
rank (lower bound): ≥ 10
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 3535403090166097125372979308
discriminant (Δ): -14141612360664388501491917232
Faltings height: 4.0805
naive height: 72.2736
primes of bad reduction: 2, 3, 13063, 437990473
regulator: 322436426.9841452804993398928718447132881113189976021884199
submitted by: David Renshaw
submitted at: 2026-10-20 21:28:13 UTC
last updated: 2026-10-20 21:28:13 UTC

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

(17915, 168226)
(19067, 1100158)
(19274, 1199405)
(21860, 2173601)
(27932, 4008863)
(34082, 5819587)
(44774, 9167195)
(54830, 12614101)
(74924, 20368415)
(197375, 87654976)

Commentary

Mordell curve y^2 = x^3 + -5721469548799. Source: N. D. Elkies, 'j=0, rank 15; also 3-rank 6 and 7 in real and imaginary quadratic fields', NMBRTHRY post, 30 Dec 2009, https://listserv.nodak.edu/cgi-bin/wa.exe?A2=NMBRTHRY;6a3fad67.0912&S=.

last edited by David Renshaw at 2026-10-20 21:28:13 UTC · history