curve #1768

y² + xy = x³ − 5118321x + 4456008297

a-invariants: [1, 0, 0, -5118321, 4456008297]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/7ℤ
conductor (N): 71058
discriminant (Δ): 2048285853033578496
Faltings height: 2.5311
naive height: 57.9586
primes of bad reduction: 2, 3, 13, 911
regulator: 3.144633053186350507522878582098657615508
submitted by: hdeping
submitted at: 2026-09-25 14:21:53 UTC
last updated: 2026-09-25 14:21:53 UTC

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

(-1794, 89583)

Commentary

Specialization t=13/1 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 08:49:51 UTC · history