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curve #4700

y² = x³ − 46111487743732324

a-invariants: [0, 0, 0, 0, -46111487743732324]
c-invariants: [0, 39840325410584727936]
rank (lower bound): ≥ 11
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 57409271152390160973432335585906352
discriminant (Δ): -918548338438242575574917369374501632
Faltings height: 5.5796
naive height: 90.2628
primes of bad reduction: 2, 3, 223, 14009, 3690091583
regulator: 49044624265.5230619241082758451475127325434271212522173807078
submitted by: jesper-petersen
submitted at: 2026-10-20 20:57:24 UTC
last updated: 2026-10-20 20:57:24 UTC

Witness: 11 independent points log in to add more points →

(366362, 55335598)
(439442, 196847242)
(446522, 207163982)
(594074, 404414930)
(2067050, 2964078974)
(3511010, 6575315974)
(3652322, 6976666618)
(3786122, 7363890718)
(5471474, 12796622890)
(8751770, 25889812526)
(13453637, 49346396773)

Commentary

Historical rank-11 Mordell curve y^2 = x^3 - 46111487743732324, attributed to Jordi Quer (1987) and documented in Tom Womack's 2003 thesis.

last edited by jesper-petersen at 2026-10-20 20:57:24 UTC · history

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