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curve #3750

y² = x³ − x² − 17997960580x + 806782918984900

a-invariants: [0, -1, 0, -17997960580, 806782918984900]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 88838909880
discriminant (Δ): 91937098974354418501883782560000
Faltings height: 4.8589
naive height: 82.4542
primes of bad reduction: 2, 3, 5, 7, 41, 43, 239, 251
regulator: 345.0721850203788458233903894338207611740142678
submitted by: Daniel Błażewicz
submitted at: 2026-10-01 07:26:09 UTC
last updated: 2026-10-01 07:26:09 UTC

Witness: 4 independent points log in to add more points →

(4190, 27045240)
(310110, 158265800)
(-10290140/169, 89967318030/2197)
(1543197160/14161, 19909434267750/1685159)

Commentary

(u,v) = (502,215) for the C2 x C4 family y^2 = x(x+u^2)(x+v^2). PARI/GP gives exact rank 4.

last edited by Daniel Błażewicz at 2026-10-01 07:26:09 UTC · history

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