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curve #5470

y² = x³ + 733257006503500

a-invariants: [0, 0, 0, 0, 733257006503500]
c-invariants: [0, -633534053619024000]
rank (lower bound): ≥ 9
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 21447058341399510566912400
discriminant (Δ): -232271641837356699439661292000000
Faltings height: 4.8893
naive height: 81.9802
primes of bad reduction: 2, 3, 5, 19, 521, 7797247
regulator: 11897442.609829152177835530630627319503433497098653800806
submitted by: jesper-petersen
submitted at: 2026-10-22 08:57:10 UTC
last updated: 2026-10-22 08:57:10 UTC

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

(-88635, 6076675)
(-84610, 11293650)
(-16435, 26996625)
(-3610, 27077850)
(33365, 27756075)
(110846, 45773394)
(839990, 770335050)
(-926535/16, 1485941075/64)
(-401090/9, 685579850/27)

Commentary

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

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

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