curve #2715

y² + xy = x³ − 6864x + 223488

a-invariants: [1, 0, 0, -6864, 223488]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/8ℤ
conductor (N): 1974
discriminant (Δ): -990247845888
Faltings height: 1.0826
naive height: 38.1625
primes of bad reduction: 2, 3, 7, 47
regulator: 1.235275546924371023389779629162531398048
submitted by: David Renshaw
submitted at: 2026-09-26 20:19:01 UTC
last updated: 2026-09-26 20:19:01 UTC

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

(54, 78)

Commentary

Cremona 1974i1 = LMFDB 1974.h5: https://www.lmfdb.org/EllipticCurve/Q/1974/h/5 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 1974, minimal discriminant -990247845888, torsion ℤ/8ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:19:02 UTC · history