curve #1761

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y² + xy + y = x³ − x² + 621237x − 226146597

a-invariants

[1, -1, 1, 621237, -226146597]

rank (lower bound)

≥ 1

torsion subgroup

ℤ/7ℤ

conductor (N)

68354

discriminant (Δ)

-37407624743081250944

Faltings height

2.4413

naive height

51.9952

primes of bad reduction

2, 11, 13, 239

regulator

8.050019047661590334242050981917971778151

submitted by

hdeping

submitted at

2026-09-25 11:26:42 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-25 11:36:16 UTC

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

(38889/25, 8290302/125)

Commentary

Specialization t=13/2 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 08:47:45 UTC · history