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curve #3745

y² = x³ + x² − 13097864x + 14682820356

a-invariants: [0, 1, 0, -13097864, 14682820356]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 34752432
discriminant (Δ): 50619260308295943373824
Faltings height: 3.0722
naive height: 60.7775
primes of bad reduction: 2, 3, 11, 13, 61, 83
regulator: 41.864055198082930839677415799931235191806344
submitted by: Daniel Błażewicz
submitted at: 2026-10-01 06:30:55 UTC
last updated: 2026-10-01 06:30:55 UTC

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

(-3920, 76194)
(-3422, 139440)
(-2930, 167076)

Commentary

(u,v) = (83,39) 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 06:30:55 UTC · history

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