curve #1747

y² + xy = x³ − 38760x + 23169600

a-invariants: [1, 0, 0, -38760, 23169600]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/7ℤ
conductor (N): 19110
discriminant (Δ): -228248616960000000
Faltings height: 2.0110
naive height: 47.4401
primes of bad reduction: 2, 3, 5, 7, 13
regulator: 1.756687476506952471715313777825798033722
submitted by: hdeping
submitted at: 2026-09-25 10:47:28 UTC
last updated: 2026-09-25 10:47:28 UTC

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

(-330, 390)

Commentary

Specialization t=8/3 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 08:46:42 UTC · history