curve #1759

← home · all curves · JSON ↓

y² + xy = x³ + 430484x + 453494672

a-invariants

[1, 0, 0, 430484, 453494672]

rank (lower bound)

≥ 1

torsion subgroup

ℤ/7ℤ

conductor (N)

69366

discriminant (Δ)

-93935597925332680704

Faltings height

2.5135

naive height

53.3880

primes of bad reduction

2, 3, 11, 1051

regulator

4.419910427424050058038709677326040411623

submitted by

hdeping

submitted at

2026-09-25 11:26:28 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-25 11:35:34 UTC

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

(176, 23036)

Commentary

Specialization t=11/3 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 08:48:01 UTC · history