curve #6200

y² = x³ + x² − 4797x + 114751

a-invariants: [0, 1, 0, -4797, 114751]
c-invariants: [230272, -100526464]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/3ℤ
conductor (N): 930644
discriminant (Δ): 1217967305984
Faltings height: 1.0554
naive height: 37.0410
primes of bad reduction: 2, 11, 13, 1627
regulator: 5.8585371887141998933554853911920058952662790
submitted by: Andrii Prokhorenkov
submitted at: 2026-10-30 15:41:41 UTC
last updated: 2026-10-30 15:41:41 UTC

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

(-78, 143)
(-67, 374)
(-39, 494)

Commentary

Specialization at T = 5/11 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 15:41:42 UTC · history