curve #5852

y² + y = x³ − 58554772030

a-invariants: [0, 0, 1, 0, -58554772030]
c-invariants: [0, 50591323033704]
rank (lower bound): ≥ 9
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 1481181693460988947870347
discriminant (Δ): -1481181693460988947870347
Faltings height: 3.3168
naive height: 63.1096
primes of bad reduction: 3, 2267, 34438919
regulator: 294036960859.83184991074338476118946526674412761651414294
submitted by: jesper-petersen
submitted at: 2026-10-25 12:06:23 UTC
last updated: 2026-10-25 12:06:23 UTC

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

(59242863622/14722569, 4589860587644429/56490497253)
(69260709460/8874441, 17068147742177531/26436959739)
(75497308762/3908529, 20659778463753953/7727161833)
(6149144739142/281333529, 15205506403885146782/4718807281917)
(78064296682/88209, 21811154713051094/26198073)
(6650002246600/426381201, -17015907615533327879/8804345419449)
(5405823500953/458559396, -12342123152245701863/9819590905944)
(154817590936/37564641, -24635422136582882/230233684689)
(275076715290385/41925019536, 4061925245360703283289/8584399300113216)

Commentary

Burkhardt parametrization (-9,2,-6), generic rank-four sextic; specialization t=298/245. The 3-isogenous partner has global minimal equation y^2+y=x^3-58554772030. PARI/GP 2.17.4 returned rank bounds [9,9].

last edited by jesper-petersen at 2026-10-25 12:06:23 UTC · history