curve #1504

y² + xy = x³ − 27221293142975272943005901584389243220x + 44819794898762860044340828149231731453878825568967424400

a-invariants: [1, 0, 0, -27221293142975272943005901584389243220, 44819794898762860044340828149231731453878825568967424400]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/8ℤ
conductor (N): 57923970284940543657510
discriminant (Δ): 423132861692420726561876599212564711444934586076190023921864325100416689024871800814765539134690064079257600000000
Faltings height: 20.5205
naive height: 270.2048
primes of bad reduction: 2, 3, 5, 7, 13, 17, 31, 37, 41, 43, 4297, 5641, 25463
regulator: 832.169674784876660089126408520578081022292
submitted by: hdeping
submitted at: 2026-09-25 00:42:42 UTC
last updated: 2026-09-25 00:42:42 UTC

(129832497108499611626741270696/31840476721, 7230613110480470482633836201327397225032628/5681582825618519)
(4610013983508219384548820172946077160/450171834634474681, 8753896909361144009808864923786913557391481651876865540/302042098733203615491466579)

Specialization t=91/296 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 08:35:16 UTC · history