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curve #3796

y² + xy + y = x³ + x² − 4568155804364150x + 114269882395884984469010

a-invariants: [1, 1, 1, -4568155804364150, 114269882395884984469010]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 33723363421605
discriminant (Δ): 460137504509636181890275376999530333972172150625
Faltings height: 7.9090
naive height: 119.7873
primes of bad reduction: 3, 5, 11, 13, 19, 29, 31, 61, 79, 191
regulator: 1806.28913359673528327671176229467149873211366375
submitted by: Daniel Błażewicz
submitted at: 2026-10-02 05:29:14 UTC
last updated: 2026-10-02 05:29:14 UTC

Witness: 5 independent points log in to add more points →

(-47097750, 474309968410)
(-46070022, 476409167083)
(14075978, 229683057563)
(54219895, 161157391244)
(13310760406/225, 762574665512401/3375)

Commentary

(u,v) = (22165,7076) for the C2 x C4 family y^2 = x(x+u^2)(x+v^2). PARI/GP gives exact rank 5.

last edited by Daniel Błażewicz at 2026-10-02 05:29:14 UTC · history

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