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curve #3744

y² = x³ − x² − 50566624x + 135581138944

a-invariants: [0, -1, 0, -50566624, 135581138944]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 6893904
discriminant (Δ): 335917957430991045279744
Faltings height: 3.2998
naive height: 64.8300
primes of bad reduction: 2, 3, 31, 41, 113
regulator: 90.221328264160824756992231893376758069096090
submitted by: Daniel Błażewicz
submitted at: 2026-10-01 06:30:22 UTC
last updated: 2026-10-01 06:30:22 UTC

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

(-7823, 228780)
(-4576, 520704)
(-169790192/29929, 2535681299760/5177717)

Commentary

(u,v) = (113,31) 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 06:30:22 UTC · history

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