curve #6188

y² = x³ − 59046732671080714812x

a-invariants: [0, 0, 0, -59046732671080714812, 0]
c-invariants: [2834243168211874310976, 0]
rank (lower bound): ≥ 12
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 774781475362237930243225457907750265632 ☆ record for quartic twists, rank ≥ 12
discriminant (Δ): 13175514620415236821389991283030211063622247281662365839060992
Faltings height: 10.4173
naive height: 148.1882
primes of bad reduction: 2, 3, 7, 29, 41, 53, 61, 157, 197, 881, 2237
regulator: 38868751983.488037205489968494533067466486429366061651055929253
submitted by: NDElkies
submitted at: 2026-10-30 15:16:08 UTC
last updated: 2026-10-30 15:16:08 UTC

(9919468701, 624757897195083)
(7911028146, 167291121762828)
(38613310050, 7435857788272620)
(421343735106, -273452926771264212)
(361151772948, 216988291677936204)
(1961005983594, -2746091753806434516)
(-65781222, 62320795756596)
(57449071050, 13645969765020180)
(31805562138, 5504206972478004)
(75399911202, -20596296538676628)
(80757348669, 22845365607624741)
(8255035194, -274064809859316)

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