curve #1024

y² + xy + y = x³ − x² + 918x + 5289

a-invariants: [1, -1, 1, 918, 5289]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/7ℤ
conductor (N): 490
discriminant (Δ): -62720000000
Faltings height: 0.7601
naive height: 32.0812
primes of bad reduction: 2, 5, 7
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:17:33 UTC
last updated: 2026-09-23 15:17:33 UTC

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Commentary

Cremona 490k2 = LMFDB 490.e2: https://www.lmfdb.org/EllipticCurve/Q/490/e/2 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 490, minimal discriminant -62720000000, torsion ℤ/7ℤ.

last edited by David Renshaw at 2026-09-23 15:17:33 UTC · history