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curve #3746

y² = x³ − x² − 41899844x + 104399119044

a-invariants: [0, -1, 0, -41899844, 104399119044]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 11067672
discriminant (Δ): 606963925636064688384
Faltings height: 3.0376
naive height: 64.2660
primes of bad reduction: 2, 3, 7, 11, 53, 113
regulator: 32.541899851612375045981652000544516932684514
submitted by: Daniel Błażewicz
submitted at: 2026-10-01 06:31:28 UTC
last updated: 2026-10-01 06:31:28 UTC

Witness: 3 independent points log in to add more points →

(-4988, 435050)
(-3406, 455616)
(-1138, 388080)

Commentary

(u,v) = (106,7) for the C2 x C4 family y^2 = x(x+u^2)(x+v^2). PARI/GP gives exact rank 3.

last edited by Daniel Błażewicz at 2026-10-01 06:31:28 UTC · history

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