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curve #1782

y² + xy = x³ − 192287115745806960x + 27179481612730522139193600

a-invariants: [1, 0, 0, -192287115745806960, 27179481612730522139193600]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/8ℤ
conductor (N): 2601162690
discriminant (Δ): 135891181772557058734964611732137249568987545600000000
Faltings height: 8.9155
naive height: 131.0069
primes of bad reduction: 2, 3, 5, 7, 17, 23, 79, 401
regulator: 41.8515739026297010640008696932344203895988
submitted by: hdeping
submitted at: 2026-09-25 14:36:04 UTC
last updated: 2026-09-25 14:36:04 UTC

Witness: 2 independent points log in to add more points →

(92020320, 3203758567440)
(7701585512130/5329, 20466102526437267180/389017)

Commentary

Specialization t=23/7 of the universal torsion Z/2xZ/8 family y^2=x(x+16t^4)(x+(t^2-1)^4).

last edited by hdeping at 2026-09-27 08:35:01 UTC · history

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