curve #2893

y² = x³ − x² − 281x + 1881

a-invariants: [0, -1, 0, -281, 1881]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 6720
discriminant (Δ): 45158400
Faltings height: 0.2636
naive height: 28.5322
primes of bad reduction: 2, 3, 5, 7
regulator: 1.05942999302328467661755677534540357709295
submitted by: David Renshaw
submitted at: 2026-09-26 20:27:10 UTC
last updated: 2026-09-26 20:27:10 UTC

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

(5, 24)
(-5, 56)

Commentary

Cremona 6720bj2 = LMFDB 6720.a2: https://www.lmfdb.org/EllipticCurve/Q/6720/a/2 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 6720, minimal discriminant 45158400, torsion ℤ/2ℤ × ℤ/2ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:27:10 UTC · history