curve #1760

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y² + xy = x³ + 411779x + 8250737

a-invariants

[1, 0, 0, 411779, 8250737]

rank (lower bound)

≥ 1

torsion subgroup

ℤ/7ℤ

conductor (N)

24882

discriminant (Δ)

-4497774542859970944

Faltings height

2.2686

naive height

50.3983

primes of bad reduction

2, 3, 11, 13, 29

regulator

4.656059403588929656652412187209883027990

submitted by

hdeping

submitted at

2026-09-25 11:26:34 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-25 11:35:58 UTC

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

(3446, 204071)

Commentary

Specialization t=11/2 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 08:47:14 UTC · history