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curve #3742

y² = x³ − x² − 16708144x + 17923062784

a-invariants: [0, -1, 0, -16708144, 17923062784]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 23893296
discriminant (Δ): 159826150187894236483584
Faltings height: 3.1569
naive height: 61.5078
primes of bad reduction: 2, 3, 7, 17, 47, 89
regulator: 54.665848553905784504360756276673201565326205
submitted by: Daniel Błażewicz
submitted at: 2026-10-01 06:28:41 UTC
last updated: 2026-10-01 06:28:41 UTC

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

(-3832, 160200)
(-430, 158202)
(12277, 1289610)

Commentary

(u,v) = (89,47) 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 06:28:41 UTC · history

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