curve #1757

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y² + xy = x³ + 110624x + 15558272

a-invariants

[1, 0, 0, 110624, 15558272]

rank (lower bound)

≥ 1

torsion subgroup

ℤ/7ℤ

conductor (N)

15918

discriminant (Δ)

-191087828767269504

Faltings height

2.0019

naive height

46.6422

primes of bad reduction

2, 3, 7, 379

regulator

2.841313466265330574461603272493996234516

submitted by

hdeping

submitted at

2026-09-25 11:26:14 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-25 11:34:40 UTC

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

(-34, 3446)

Commentary

Specialization t=9/2 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 08:46:10 UTC · history