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curve #5471

y² = x³ − 19797939175594500

a-invariants: [0, 0, 0, 0, -19797939175594500]
c-invariants: [0, 17105419447713648000]
rank (lower bound): ≥ 9
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 21447058341399510566912400
discriminant (Δ): -169326026899433033891513081868000000
Faltings height: 5.4386
naive height: 88.5719
primes of bad reduction: 2, 3, 5, 19, 521, 7797247
regulator: 35692327.829487456533506591891881958510300491295961402418
submitted by: jesper-petersen
submitted at: 2026-10-22 08:57:41 UTC
last updated: 2026-10-22 08:57:41 UTC

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

(369930, 175574250)
(386346, 194600394)
(403066, 213740614)
(504930, 330054750)
(927021, 881393319)
(1639605, 2094745725)
(14606706, 55824784146)
(1693641/4, 1894994811/8)
(2604729/4, 4050309933/8)

Commentary

Rank-9 Mordell curve arising from Mestre's polynomial cube-completion construction using the integer sextuple (-30,-17,-5,1,22,29).

last edited by jesper-petersen at 2026-10-22 08:57:41 UTC · history

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