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curve #1783

y² + xy = x³ − 11690287988320x − 8201500993088281600

a-invariants: [1, 0, 0, -11690287988320, -8201500993088281600]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/8ℤ
conductor (N): 36278970
discriminant (Δ): 73189875885488900316097964994585600000000
Faltings height: 6.5384
naive height: 101.8829
primes of bad reduction: 2, 3, 5, 7, 13, 97, 137
regulator: 12.73210820610761561305653538838086233319
submitted by: hdeping
submitted at: 2026-09-25 14:36:10 UTC
last updated: 2026-09-25 14:36:10 UTC

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

(-21691494617440/10621081, 92625057142647371840/34614102979)

Commentary

Specialization t=9/4 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 08:54:07 UTC · history

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