curve #5784

y² = x³ + 1784403915192

a-invariants: [0, 0, 0, 0, 1784403915192]
c-invariants: [0, -1541724982725888]
rank (lower bound): ≥ 9
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 117929530835279197348032
discriminant (Δ): -1375530047662696557867445248
Faltings height: 3.8863
naive height: 69.9434
primes of bad reduction: 2, 3, 41, 907, 222151
regulator: 7655803.4917559062801382285858085029114358675268467727770
submitted by: jesper-petersen
submitted at: 2026-10-25 08:03:57 UTC
last updated: 2026-10-25 08:03:57 UTC

Witness: 9 independent points log in to add more points →

(-11226, 608004)
(-10398, 812520)
(-9246, 996984)
(-5223, 1281375)
(-4922, 1290412)
(-1466, 1334636)
(1702, 1337660)
(1977, 1338705)
(5638, 1401292)

Commentary

Specialization at t=64/163 of the rank-four sextic Mordell family f(t) = 6174784t^6 − 12102720t^5 + 10989213t^4 − 5815388t^3 + 1819860t^2 − 334464t + 36352. The specialization was identified using a 328-prime Mestre–Nagao score of approximately 54.02. PARI/GP 2.17.4 returned matching rank bounds [9,9].

last edited by jesper-petersen at 2026-10-25 08:03:57 UTC · history