curve #1752

y² + xy + y = x³ − x² − 360168x + 989505963

a-invariants: [1, -1, 1, -360168, 989505963]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/7ℤ
conductor (N): 245938
discriminant (Δ): -419913591310978924544
Faltings height: 2.6369
naive height: 54.9484
primes of bad reduction: 2, 7, 11, 1597
regulator: 2.967781072037125179028500925332740705951
submitted by: hdeping
submitted at: 2026-09-25 10:48:04 UTC
last updated: 2026-09-25 10:48:04 UTC

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

(-959, 21745)

Commentary

Specialization t=11/4 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 08:49:04 UTC · history