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curve #1826

y² = x³ − x² − 343633641057979504x + 36692720733182921224013824

a-invariants: [0, -1, 0, -343633641057979504, 36692720733182921224013824]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 513997018590645744
discriminant (Δ): 2015344692559007799804936253481623637014756953669832704
Faltings height: 9.1154
naive height: 132.7487
primes of bad reduction: 2, 3, 7, 11, 31, 71, 73, 79, 89, 257, 479
regulator: 63772.892294225714961747828864143445623019495780807
submitted by: dujella
submitted at: 2026-09-25 15:29:32 UTC
last updated: 2026-09-25 15:29:32 UTC

Witness: 6 independent points log in to add more points →

(-7755736, 6273546526104)
(69795322, 3612298454310)
(-607838712, 4581447129560)
(106344040, 1162747450008)
(3003675688, 161566995145320)
(582225800, 5829859131432)

Commentary

found by Dujella (2006)

last edited by dujella at 2026-09-25 15:29:32 UTC · history

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