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curve #5468

y² = x³ − 29614783057896036

a-invariants: [0, 0, 0, 0, -29614783057896036]
c-invariants: [0, 25587172562022175104]
rank (lower bound): ≥ 9
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 161657109345237320263136688
discriminant (Δ): -378879282244618310341005257309743872
Faltings height: 5.5058
naive height: 89.3772
primes of bad reduction: 2, 3, 7, 11, 13, 19, 10721279
regulator: 255068224.26519494482021521263797949206562779036361387364
submitted by: jesper-petersen
submitted at: 2026-10-22 08:37:51 UTC
last updated: 2026-10-22 08:37:51 UTC

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

(340690, 99644342)
(639730, 481868842)
(955738, 918362606)
(1115053, 1164808471)
(1288105/4, 491829611/8)
(2927197/9, 1868812127/27)
(7889674/25, 5327025782/125)
(685038445/2209, 1499707504841/103823)
(2646874791925/7612081, 2341279399889759693/21001731479)

Commentary

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

last edited by jesper-petersen at 2026-10-22 08:37:52 UTC · history

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