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curve #1781

y² + xy = x³ − 68498472650432440x + 6597012171547236617921600

a-invariants: [1, 0, 0, -68498472650432440, 6597012171547236617921600]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/8ℤ
conductor (N): 44245640670
discriminant (Δ): 1768561927045055047002658300206667798876185600000000
Faltings height: 8.5924
naive height: 127.9104
primes of bad reduction: 2, 3, 5, 7, 11, 19, 47, 89, 241
regulator: 40.0419017847502058231867871116711343058457
submitted by: hdeping
submitted at: 2026-09-25 14:35:56 UTC
last updated: 2026-09-25 14:35:56 UTC

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

(33900142628/289, 2061207821164888/4913)
(21526744060910/73441, 68081967084010895180/19902511)

Commentary

Specialization t=15/4 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 08:34:44 UTC · history

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