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curve #5413

y² = x³ + 1959373119356649

a-invariants: [0, 0, 0, 0, 1959373119356649]
c-invariants: [0, -1692898375124144736]
rank (lower bound): ≥ 9
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 5451618715945823931151788
discriminant (Δ): -1658509785010398998086701339974832
Faltings height: 5.0532
naive height: 83.9459
primes of bad reduction: 2, 3, 17, 19, 383, 1816141
regulator: 3008806.0188690621718804938796333401942786773411805631108
submitted by: jesper-petersen
submitted at: 2026-10-21 22:18:35 UTC
last updated: 2026-10-21 22:18:35 UTC

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

(-124602, 4984479)
(-104550, 28575657)
(-82365, 37424718)
(-38760, 43602093)
(1938, 44264889)
(6528, 44267949)
(67260, 47577843)
(243048, 127737171)
(313140, 180734157)

Commentary

Rank-9 Mordell curve found through Mestre's polynomial cube-completion construction, starting from the integer sextuple (-49,-31,-5,7,29,49).

last edited by jesper-petersen at 2026-10-21 22:18:35 UTC · history

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