curve #4701

y² + y = x³ − 102092055385293546

a-invariants: [0, 0, 1, 0, -102092055385293546]
c-invariants: [0, 88207535852893623528]
rank (lower bound): ≥ 12
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 1500881439282313662166917441111457401
discriminant (Δ): -4502644317846940986500752323334372203
Faltings height: 5.7120
naive height: 91.8524
primes of bad reduction: 3, 29, 163, 443, 195012572003
regulator: 181995421083.74198433425206247249941288636241951940218533569934
submitted by: jesper-petersen
submitted at: 2026-10-20 21:01:56 UTC
last updated: 2026-10-20 21:01:56 UTC

Witness: 12 independent points log in to add more points →

(479796, 91427565)
(527456, 211308754)
(635072, 392483026)
(2609513/4, 3351975359/8)
(725702, 529239178)
(769712, 594919213)
(3112049/4, 4858583435/8)
(3565313/4, 6227875283/8)
(960692, 885753106)
(1419276, 1660366994)
(7311737/4, 19605165671/8)
(1886166, 2570636874)

Commentary

Historical rank-12 Mordell curve y^2 = x^3 - 6533891544658786928, attributed to Jordi Quer (1987), "Corps quadratiques de 3-rang 6 et courbes elliptiques de rang 12", C. R. Acad. Sci. Paris 305, 215–218.

last edited by jesper-petersen at 2026-10-20 21:01:56 UTC · history