curve #1751

y² + xy = x³ − 1330145x + 291422025

a-invariants: [1, 0, 0, -1330145, 291422025]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/7ℤ
conductor (N): 32370
discriminant (Δ): 113901735543570000000
Faltings height: 2.5444
naive height: 53.9160
primes of bad reduction: 2, 3, 5, 13, 83
regulator: 1.375890209125746958161434616676630825130
submitted by: hdeping
submitted at: 2026-09-25 10:47:57 UTC
last updated: 2026-09-25 10:47:57 UTC

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

(-1250, 1795)

Commentary

Specialization t=15/2 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 08:48:32 UTC · history