curve #2766

y² = x³ − x² − 14x + 24

a-invariants: [0, -1, 0, -14, 24]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 672
discriminant (Δ): 28224
Faltings height: -0.4052
naive height: 19.6014
primes of bad reduction: 2, 3, 7
regulator: 0.9931091614598024517938796376206598194188
submitted by: David Renshaw
submitted at: 2026-09-26 20:21:27 UTC
last updated: 2026-09-26 20:21:27 UTC

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

(4, 4)

Commentary

Cremona 672e1 = LMFDB 672.b3: https://www.lmfdb.org/EllipticCurve/Q/672/b/3 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 672, minimal discriminant 28224, torsion ℤ/2ℤ × ℤ/2ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:21:27 UTC · history