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curve #3743

y² = x³ − x² − 21263320x + 36967992832

a-invariants: [0, -1, 0, -21263320, 36967992832]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 6966960
discriminant (Δ): 25121723782755600000000
Faltings height: 3.0835
naive height: 62.2311
primes of bad reduction: 2, 3, 5, 7, 11, 13, 29
regulator: 5.9962109091331935451048670262682053798481000
submitted by: Daniel Błażewicz
submitted at: 2026-10-01 06:29:27 UTC
last updated: 2026-10-01 06:29:27 UTC

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

(-5156, 97500)
(-4906, 152250)
(-18779/9, 7257250/27)

Commentary

(u,v) = (91,25) 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 06:29:27 UTC · history

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