curve #6199

y² = x³ + x² − 6426x + 195265

a-invariants: [0, 1, 0, -6426, 195265]
c-invariants: [308464, -170559712]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/3ℤ
conductor (N): 530740
discriminant (Δ): 150316182800
Faltings height: 0.9908
naive height: 37.9181
primes of bad reduction: 2, 5, 7, 17, 223
regulator: 2.7020230477757624872127092105500567023386103
submitted by: Andrii Prokhorenkov
submitted at: 2026-10-30 15:41:35 UTC
last updated: 2026-10-30 15:41:35 UTC

Witness: 3 independent points log in to add more points →

(-63, 595)
(112, 945)
(28/9, 11305/27)

Commentary

Specialization at T = -5/7 of the elliptic fibration of X648 given by: y^2 + (Lx+B)y = x^3, where L = -152T^2 + 280T - 200, B = 432000T^5 - 1539000T^4 + 1782000T^3 - 675000T^2.

last edited by Andrii Prokhorenkov at 2026-10-30 15:41:35 UTC · history