curve #3054

y² + xy = x³ + 83616x − 29981952

a-invariants: [1, 0, 0, 83616, -29981952]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/8ℤ
conductor (N): 6006
discriminant (Δ): -425928037217050368
Faltings height: 2.0645
naive height: 47.9558
primes of bad reduction: 2, 3, 7, 11, 13
regulator: 2.554040933166269306961422812577984875390
submitted by: David Renshaw
submitted at: 2026-09-26 20:35:08 UTC
last updated: 2026-09-26 20:35:08 UTC

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

(246, 2220)

Commentary

Cremona 6006bd1 = LMFDB 6006.bb6: https://www.lmfdb.org/EllipticCurve/Q/6006/bb/6 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 6006, minimal discriminant -425928037217050368, torsion ℤ/8ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:35:08 UTC · history