curve #5472

y² + y = x³ − 773390528404669

a-invariants: [0, 0, 1, 0, -773390528404669]
c-invariants: [0, 668209416541633800]
rank (lower bound): ≥ 10
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 10335736674882191357895573456075
discriminant (Δ): -258393416872054783947389336401875
Faltings height: 4.8982
naive height: 82.0868
primes of bad reduction: 3, 5, 47, 1129, 777330623
regulator: 309272542397.5874435286236396176865705105338270086241829166
submitted by: jesper-petersen
submitted at: 2026-10-22 08:58:19 UTC
last updated: 2026-10-22 08:58:19 UTC

Witness: 10 independent points log in to add more points →

(2036209/16, 2296652841/64)
(36992809/400, 33563048373/8000)
(122274841/1296, 380322243683/46656)
(51607381/529, 151517343033/12167)
(105077209/225, 1073019646052/3375)
(186575149/1681, 1679597747784/68921)
(277758409/2209, 3618348227028/103823)
(1606748869/1369, 64389952137464/50653)
(6576877939/53361, 408627074635030/12326391)
(52592090881/345744, 10653722912546335/203297472)

Commentary

Rank-10 elliptic curve with j-invariant 0, arising from Mestre's polynomial cube-completion construction using the integer sextuple (-111,-9,-1,11,51,59).

last edited by jesper-petersen at 2026-10-22 08:58:19 UTC · history