curve #1749

y² + xy + y = x³ − x² − 450273x + 116420913

a-invariants: [1, -1, 1, -450273, 116420913]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/7ℤ
conductor (N): 10766
discriminant (Δ): -1328135939293184
Faltings height: 1.9219
naive height: 50.6667
primes of bad reduction: 2, 7, 769
regulator: 3.091150269156805906062455600585450367700
submitted by: hdeping
submitted at: 2026-09-25 10:47:42 UTC
last updated: 2026-09-25 10:47:42 UTC

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

(-177, 13892)

Commentary

Specialization t=-7/1 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 08:47:30 UTC · history