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curve #1787

y² + xy = x³ − 230865939670540x + 31001950145310419600

a-invariants: [1, 0, 0, -230865939670540, 31001950145310419600]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/8ℤ
conductor (N): 1038338070
discriminant (Δ): 787101126295770368467023601331142681600000000
Faltings height: 7.3042
naive height: 110.8322
primes of bad reduction: 2, 3, 5, 7, 11, 17, 137, 193
regulator: 9.735509916663982526044442933915459841423
submitted by: hdeping
submitted at: 2026-09-25 14:36:43 UTC
last updated: 2026-09-25 14:36:43 UTC

Witness: 1 independent point log in to add more points →

(-128464679080/10201, 31614556926965860/1030301)

Commentary

Specialization t=11/4 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 08:55:28 UTC · history

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