curve #4749

y² = x³ + 3612077876156

a-invariants: [0, 0, 0, 0, 3612077876156]
c-invariants: [0, -3120835284998784]
rank (lower bound): ≥ 10
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 352271877752222271180081072 ☆ record for Mordell curves, rank ≥ 10
discriminant (Δ): -5636350044035556338881297152 ☆ record for Mordell curves, rank ≥ 10
Faltings height: 4.0038 ☆ record for Mordell curves, rank ≥ 10
naive height: 71.3538 ☆ record for Mordell curves, rank ≥ 10
primes of bad reduction: 2, 3, 903019469039
regulator: 197328167.5744387724375000930625680603152338476507245396628
submitted by: David Renshaw
submitted at: 2026-10-20 21:28:09 UTC
last updated: 2026-10-20 21:28:09 UTC

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

(-14203, 864277)
(-13795, 993409)
(-11158, 1490938)
(-5155, 1864159)
(-2443, 1896707)
(4802, 1929458)
(8117, 2036387)
(9002, 2083642)
(71045, 19031659)
(93122, 28480498)

Commentary

Mordell curve y^2 = x^3 + 3612077876156. 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 21:28:09 UTC · history