curve #2722

y² = x³ + x² − 24400x + 1458548

a-invariants: [0, 1, 0, -24400, 1458548]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/8ℤ
conductor (N): 1680
discriminant (Δ): 453600000000
Faltings height: 1.2177
naive height: 41.9207
primes of bad reduction: 2, 3, 5, 7
regulator: 1.804705305068544727017699846541670889461
submitted by: David Renshaw
submitted at: 2026-09-26 20:19:21 UTC
last updated: 2026-09-26 20:19:21 UTC

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

(92, 30)

Commentary

Cremona 1680h5 = LMFDB 1680.p1: https://www.lmfdb.org/EllipticCurve/Q/1680/p/1 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 1680, minimal discriminant 453600000000, torsion ℤ/8ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:19:21 UTC · history