curve #1501

y² + xy = x³ − 103261464630444172572903933816814229471272130x + 403780767639707610641424464011353774314390587505020052993877000900

a-invariants: [1, 0, 0, -103261464630444172572903933816814229471272130, 403780767639707610641424464011353774314390587505020052993877000900]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/8ℤ
conductor (N): 1755993439796026473773085810
discriminant (Δ): 35657339933816659907695978906711920579802632136113566667148425809728557061477259839339496096109386045505165295795555857152100000000
Faltings height: 24.0298
naive height: 315.6511
primes of bad reduction: 2, 3, 5, 7, 13, 17, 19, 23, 59, 79, 137, 223, 431, 701, 769, 2617
regulator: 19.93213892225664213447947095515366802102
submitted by: hdeping
submitted at: 2026-09-25 00:42:19 UTC
last updated: 2026-09-25 00:42:19 UTC

(301587049333006815038390992540/55071241, 20529548303614678487340832148668877382925670/408683679461)

Specialization t=153/1027 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 08:56:17 UTC · history