curve #5785

y² = x³ − 66089033896

a-invariants: [0, 0, 0, 0, -66089033896]
c-invariants: [0, 57100925286144]
rank (lower bound): ≥ 9
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 117929530835279197348032
discriminant (Δ): -1886872493364467157568512
Faltings height: 3.3370
naive height: 63.3517
primes of bad reduction: 2, 3, 41, 907, 222151
regulator: 150689180128.23150331196075325446876280579218053092502857
submitted by: jesper-petersen
submitted at: 2026-10-25 08:04:50 UTC
last updated: 2026-10-25 08:04:50 UTC

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

(17663211758/3500641, 1635727420177364/6549699311)
(18559878074/3003289, 2145466093805080/5204699837)
(19590089018/2374681, 2575483558902664/3659383421)
(86359674521/3031081, 25342246143844625/5277112021)
(1754593718830/54508689, 2321849942564679676/402437650887)
(1783616249518/4835601, 2382055327238432444/10633486599)
(1785636505294/6517809, -2386101347957810060/16639966377)
(88214108921/434281, -26200245755987935/286191179)
(1829207753710/71520849, -2469079300884945436/604851819993)

Commentary

The rationally 3-isogenous partner of the specialization t=64/163 of the rank-four sextic Mordell family obtained through the Burkhardt parametrization.

last edited by jesper-petersen at 2026-10-25 08:04:50 UTC · history