curve #3047

y² + xy + y = x³ − 8133x − 78944

a-invariants: [1, 0, 1, -8133, -78944]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/6ℤ
conductor (N): 43230
discriminant (Δ): 31777292250000
Faltings height: 1.2821
naive height: 38.6245
primes of bad reduction: 2, 3, 5, 11, 131
regulator: 2.42471271300442013002232140266781891846435
submitted by: David Renshaw
submitted at: 2026-09-26 20:34:48 UTC
last updated: 2026-09-26 20:34:48 UTC

Witness: 2 independent points log in to add more points →

(95, 42)
(-80, 287)

Commentary

Cremona 43230o1 = LMFDB 43230.n4: https://www.lmfdb.org/EllipticCurve/Q/43230/n/4 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 43230, minimal discriminant 31777292250000, torsion ℤ/6ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:34:48 UTC · history