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curve #3590

y² = x³ − x² − 80087385824x + 8192057426724864

a-invariants: [0, -1, 0, -80087385824, 8192057426724864]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 42043148112
discriminant (Δ): 3884250278458477756167588826988544
Faltings height: 5.1936
naive height: 86.9328
primes of bad reduction: 2, 3, 7, 29, 103, 163, 257
regulator: 5956.239403384666045032457882650102533004340774
submitted by: Daniel Błażewicz
submitted at: 2026-09-29 04:49:16 UTC
last updated: 2026-09-29 04:49:16 UTC

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

(-92228416/289, 173624418240/4913)
(23968016/25, 112681329264/125)
(3620380688/5929, 197402414891760/456533)
(45836593616/390625, 4944321215651664/244140625)

Commentary

(u,v) = (721,257) 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 08:24:38 UTC · history

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