curve #2762

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: 1.791491821865470794505102599041959982905
submitted by: David Renshaw
submitted at: 2026-09-26 20:21:18 UTC
last updated: 2026-09-26 20:21:18 UTC

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

(6, 12)

Commentary

Cremona 672f1 = LMFDB 672.f3: https://www.lmfdb.org/EllipticCurve/Q/672/f/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 20:21:18 UTC · history