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curve #3774

y² = x³ − x² − 176464447760644x + 885964287175736338564

a-invariants: [0, -1, 0, -176464447760644, 885964287175736338564]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 560334579081816
discriminant (Δ): 12592323423666696033407474749863936876259584
Faltings height: 7.0603
naive height: 110.0260
primes of bad reduction: 2, 3, 7, 11, 17, 29, 41, 59, 71, 3581
regulator: 1165.32494482326953110040806277347878946306905574
submitted by: Daniel Błażewicz
submitted at: 2026-10-01 19:46:41 UTC
last updated: 2026-10-01 19:46:41 UTC

Witness: 5 independent points log in to add more points →

(6070225, 6201512892)
(11838478, 21355354440)
(565795378, 13454588596680)
(2282446/9, 783106275952/27)
(205079554/169, 57021087067560/2197)

Commentary

(u,v) = (4879,1298) for the C2 x C4 family y^2 = x(x+u^2)(x+v^2). PARI/GP gives exact rank 5.

last edited by Daniel Błażewicz at 2026-10-01 19:46:42 UTC · history

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