curve #2885

y² = x³ − x² − 190x − 800

a-invariants: [0, -1, 0, -190, -800]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 43680
discriminant (Δ): 119246400
Faltings height: 0.2728
naive height: 27.3599
primes of bad reduction: 2, 3, 5, 7, 13
regulator: 3.10511747103844780266198062247745345681630
submitted by: David Renshaw
submitted at: 2026-09-26 20:26:51 UTC
last updated: 2026-09-26 20:26:51 UTC

Witness: 2 independent points log in to add more points →

(-8, 12)
(-9, 10)

Commentary

Cremona 43680f1 = LMFDB 43680.o3: https://www.lmfdb.org/EllipticCurve/Q/43680/o/3 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 43680, minimal discriminant 119246400, torsion ℤ/2ℤ × ℤ/2ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:26:51 UTC · history