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curve #3741

y² + xy + y = x³ + x² − 32658455x + 71822257652

a-invariants: [1, 1, 1, -32658455, 71822257652]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 7877415
discriminant (Δ): 2457387270123192225
Faltings height: 2.8479
naive height: 63.5184
primes of bad reduction: 3, 5, 7, 13, 29, 199
regulator: 62.853457703442281464136427796925516036384567
submitted by: Daniel Błażewicz
submitted at: 2026-10-01 06:24:59 UTC
last updated: 2026-10-01 06:24:59 UTC

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

(1932, 125296)
(3557, 24221)
(42902, 8789771)

Commentary

(u,v) = (199,4) 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 06:24:59 UTC · history

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