curve #5795

y² = x³ + 25773934584321913500

a-invariants: [0, 0, 0, 0, 25773934584321913500]
c-invariants: [0, -22268679480854133264000]
rank (lower bound): ≥ 11
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 16395531589168839108088089130800
discriminant (Δ): -286975744109383049872207169602240332000000
Faltings height: 6.6339
naive height: 102.9149
primes of bad reduction: 2, 3, 5, 7, 1855374479669
regulator: 16467018210.9372829510428819807670064691362853530740557412368
submitted by: jesper-petersen
submitted at: 2026-10-25 10:33:35 UTC
last updated: 2026-10-25 10:33:35 UTC

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

(-2953566, 91365498)
(-1095435, 4945648275)
(911565, 5150864025)
(2965165, 7200296425)
(94602690, 920156797350)
(106610490, 1100790132750)
(128287026, 1453037279274)
(-29725335/16, 281611190475/64)
(17305785/4, 82658603475/8)
(19810665/16, 336667459275/64)
(98443114/25, 1164789484138/125)

Commentary

Specialization t = 392/505 of a generic rank-four Burkhardt Mordell family with construction parameters (-9, 5, -5). The specialization was identified using a 328-prime Mestre–Nagao sieve across multiple Burkhardt families. PARI/GP 2.17.4 returned matching computational rank bounds [11,11].

last edited by jesper-petersen at 2026-10-25 10:33:36 UTC · history