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curve #1780

y² + xy = x³ − 29935688890228090x + 1981971871537597930302692

a-invariants: [1, 0, 0, -29935688890228090, 1981971871537597930302692]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/8ℤ
conductor (N): 44941883910
discriminant (Δ): 19923042016357631752615257584464135090742996640000
Faltings height: 8.2944
naive height: 125.4271
primes of bad reduction: 2, 3, 5, 7, 11, 17, 41, 103, 271
regulator: 45.1871789295164249442038260630405357888706
submitted by: hdeping
submitted at: 2026-09-25 14:35:49 UTC
last updated: 2026-09-25 14:35:49 UTC

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

(-242200815124/2209, 206248697140351234/103823)
(184563415196/289, 76635811544920654/4913)

Commentary

Specialization t=17/11 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 08:34:28 UTC · history

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