curve #1503

y² + xy = x³ − 3069679751784694380786055967304857907280x − 62254100459808747804135701726270242050145766534506409977600

a-invariants: [1, 0, 0, -3069679751784694380786055967304857907280, -62254100459808747804135701726270242050145766534506409977600]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/8ℤ
conductor (N): 9619387484661599521170
discriminant (Δ): 176977351034673494641803936742953766466033032761568677189291243096946820262138642081197066355246900667186319385600000000
Faltings height: 21.6369
naive height: 284.3808
primes of bad reduction: 2, 3, 5, 7, 17, 31, 103, 137, 167, 193, 257, 769, 967
regulator: 1161.73735416663632386039608321050232828896
submitted by: hdeping
submitted at: 2026-09-25 00:42:33 UTC
last updated: 2026-09-25 00:42:33 UTC

(-14086555299442611970467648160/422590249, 478299514584413064114567011507799186115760/8687187748693)
(-9598217286273952351805705359605286432990022512/282011909051014396321544569, 250466476470535773820897723530248811374171929704300732008430904253168/4735885269525082702835590163535804018253)

Specialization t=245/579 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 08:35:33 UTC · history