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curve #3748

y² = x³ − x² − 13076969284x + 337803830646724

a-invariants: [0, -1, 0, -13076969284, 337803830646724]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 25662342552
discriminant (Δ): 93825450822607886814843160721664
Faltings height: 4.8343
naive height: 81.4960
primes of bad reduction: 2, 3, 7, 11, 19, 23, 43, 739
regulator: 164.2676673939887615136582023948741392622496948
submitted by: Daniel Błażewicz
submitted at: 2026-10-01 07:07:28 UTC
last updated: 2026-10-01 07:07:28 UTC

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

(-4780, 20005062)
(-3049756/25, 1355770878/125)
(-1683710/289, 99939681864/4913)
(6144916/49, 8878938678/343)

Commentary

(u,v) = (473,266) 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 07:07:28 UTC · history

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