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curve #5469

y² = x³ + 799599142563192972

a-invariants: [0, 0, 0, 0, 799599142563192972]
c-invariants: [0, -690853659174598727808]
rank (lower bound): ≥ 9
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 161657109345237320263136688
discriminant (Δ): -276202996756326748238592832578803282688
Faltings height: 6.0551
naive height: 95.9689
primes of bad reduction: 2, 3, 7, 11, 13, 19, 10721279
regulator: 85022741.421731648273405070879326497355209263454537957881
submitted by: jesper-petersen
submitted at: 2026-10-22 08:38:29 UTC
last updated: 2026-10-22 08:38:29 UTC

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

(-915642, 178674678)
(-902538, 253799910)
(-830466, 476286174)
(277069, 906018191)
(1557829, 2140137181)
(1979838, 2925762462)
(5430789, 12687490179)
(34114158, 199253683278)
(-28107639/100, 881698928859/1000)

Commentary

Rank-9 Mordell curve discovered through Mestre's polynomial cube-completion construction from the integer sextuple (-15,-14,-11,6,15,19).

last edited by jesper-petersen at 2026-10-22 08:38:29 UTC · history

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