curve #1769

y² + xy + y = x³ − x² − 5582262x + 5077966149

a-invariants: [1, -1, 1, -5582262, 5077966149]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/7ℤ
conductor (N): 4730
discriminant (Δ): -360317791790000000
Faltings height: 2.4932
naive height: 58.2189
primes of bad reduction: 2, 5, 11, 43
regulator: 0.9820573051492007438543485896172307604395
submitted by: hdeping
submitted at: 2026-09-25 14:22:01 UTC
last updated: 2026-09-25 14:22:01 UTC

Witness: 1 independent point log in to add more points →

(-2493, 60371)

Commentary

Specialization t=-10/1 of the universal X_1(7) Tate normal form family y^2+(-t^2+t+1)xy+(-t^3+t^2)y=x^3+(-t^3+t^2)x^2 (K3 elliptic surface, rational 7-torsion point (0,0)).

last edited by hdeping at 2026-09-27 08:50:07 UTC · history