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curve #3753

y² + xy = x³ − 5924609140x + 142661679026975

a-invariants: [1, 0, 0, -5924609140, 142661679026975]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 10405407855
discriminant (Δ): 4517140598198167496534000150625
Faltings height: 4.5987
naive height: 79.1207
primes of bad reduction: 3, 5, 17, 19, 59, 89, 409
regulator: 1818.936752479595055864478866793368619204949847
submitted by: Daniel Błażewicz
submitted at: 2026-10-01 08:50:38 UTC
last updated: 2026-10-01 08:50:38 UTC

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

(4144430, 8433659285)
(-1364539/16, 339210503/64)
(24217369/64, 116748093719/512)
(200280145/2304, 1860576763745/110592)

Commentary

(u,v) = (765,356) 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 08:50:38 UTC · history

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