curve #3176

y² = x³ − x² − 49520x + 4165632

a-invariants: [0, -1, 0, -49520, 4165632]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 305040
discriminant (Δ): 334977845760000
Faltings height: 1.5704
naive height: 44.0440
primes of bad reduction: 2, 3, 5, 31, 41
regulator: 3.9296421030520191182456382134416567036404786
submitted by: David Renshaw
submitted at: 2026-09-26 20:40:59 UTC
last updated: 2026-09-26 20:40:59 UTC

Witness: 3 independent points log in to add more points →

(154, 410)
(72, 984)
(149, 270)

Commentary

Cremona 305040s2 = LMFDB 305040.s3: https://www.lmfdb.org/EllipticCurve/Q/305040/s/3 Mordell–Weil rank exactly 3 (Cremona's tables). Conductor 305040, minimal discriminant 334977845760000, torsion ℤ/2ℤ × ℤ/2ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:40:59 UTC · history