curve #3286

y² = x³ − 242x + 1449

a-invariants: [0, 0, 0, -242, 1449]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/4ℤ
conductor (N): 1160
discriminant (Δ): 11600
Faltings height: -0.0437
naive height: 28.0804
primes of bad reduction: 2, 5, 29
regulator: 2.887925779477907941407491707052839950256
submitted by: David Renshaw
submitted at: 2026-09-26 20:51:45 UTC
last updated: 2026-09-26 20:51:45 UTC

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

(-16, 35)

Commentary

Cremona 1160c1 = LMFDB 1160.b3: https://www.lmfdb.org/EllipticCurve/Q/1160/b/3 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 1160, minimal discriminant 11600, torsion ℤ/4ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:51:46 UTC · history