curve #1502

y² + xy = x³ − 146021374755300816170603848860877389490x + 679160767177079375741753235895987223321309153812990708100

a-invariants: [1, 0, 0, -146021374755300816170603848860877389490, 679160767177079375741753235895987223321309153812990708100]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/8ℤ
conductor (N): 31761454582842251479170
discriminant (Δ): 158475870772909920454951934538069295217408835430795777133451466760714425760645073121478594064906048464100000000
Faltings height: 20.4841
naive height: 275.2441
primes of bad reduction: 2, 3, 5, 7, 17, 23, 29, 31, 191, 331, 569, 3329, 3593
regulator: 27.25658808229588457365281228751821109167
submitted by: hdeping
submitted at: 2026-09-25 00:42:26 UTC
last updated: 2026-09-25 00:42:26 UTC

(23414737123396903311356189401220/211464781609, 112652824670651104879871862563588761884439141670/97242714217243477)

Specialization t=21/310 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 08:56:01 UTC · history