curve #3058

y² + xy = x³ − 269700x + 54090000

a-invariants: [1, 0, 0, -269700, 54090000]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/8ℤ
conductor (N): 39270
discriminant (Δ): -9447183900000000
Faltings height: 1.9187
naive height: 49.1363
primes of bad reduction: 2, 3, 5, 7, 11, 17
regulator: 1.723225176077998579661760446581140614966
submitted by: David Renshaw
submitted at: 2026-09-26 20:35:17 UTC
last updated: 2026-09-26 20:35:17 UTC

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

(282, 552)

Commentary

Cremona 39270cv1 = LMFDB 39270.ct6: https://www.lmfdb.org/EllipticCurve/Q/39270/ct/6 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 39270, minimal discriminant -9447183900000000, torsion ℤ/8ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:35:17 UTC · history