curve #2987

y² = x³ + x² − 4x + 32

a-invariants: [0, 1, 0, -4, 32]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/4ℤ
conductor (N): 552
discriminant (Δ): -476928
Faltings height: -0.2305
naive height: 20.5407
primes of bad reduction: 2, 3, 23
regulator: 0.8270783900387450210415778111445865896499
submitted by: David Renshaw
submitted at: 2026-09-26 20:32:03 UTC
last updated: 2026-09-26 20:32:03 UTC

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

(-2, 6)

Commentary

Cremona 552e1 = LMFDB 552.e4: https://www.lmfdb.org/EllipticCurve/Q/552/e/4 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 552, minimal discriminant -476928, torsion ℤ/4ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:32:03 UTC · history