curve #6216

y² + y = x³ + 223791194925838

a-invariants: [0, 0, 1, 0, 223791194925838]
c-invariants: [0, -193355592415924248]
rank (lower bound): ≥ 11
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 7211879845392172563924114983481
discriminant (Δ): -21635639536176517691772344950443 ☆ record for Mordell curves, rank ≥ 11
Faltings height: 4.6915 ☆ record for Mordell curves, rank ≥ 11
naive height: 79.6066 ☆ record for Mordell curves, rank ≥ 11
primes of bad reduction: 3, 281947, 3174939899
regulator: 25805493215.3162600332925666171913473102227786644503391644769
submitted by: jesper-petersen
submitted at: 2026-10-30 22:10:20 UTC
last updated: 2026-10-30 22:10:20 UTC

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

(-60146, 2492098)
(178321/4, 141396443/8)
(63604, 21933973)
(72118, 24471970)
(98324, 34268778)
(257788, 131738389)
(271988, 142635114)
(-6151886/625, 233245999138/15625)
(-3495743/64, 3993340895/512)
(5984737/16, 14672165263/64)
(22290136/3249, 2772420829498/185193)

Commentary

Generic-rank-4 Burkhardt fibration associated with quartic coordinates (8, 13, 31, 16, -14), specialized at t=8364/10145. PARI/GP 2.17.4 returned rank bounds [11,11].

last edited by jesper-petersen at 2026-10-30 22:10:20 UTC · history