curve #895

y² + xy = x³ − 39x + 90

a-invariants: [1, 0, 0, -39, 90]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/8ℤ
conductor (N): 21
discriminant (Δ): 45927
Faltings height: -0.2724
naive height: 22.6059
primes of bad reduction: 3, 7
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 14:57:08 UTC
last updated: 2026-09-23 14:57:08 UTC

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Commentary

Cremona 21a3 = LMFDB 21.a3: https://www.lmfdb.org/EllipticCurve/Q/21/a/3 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 21, minimal discriminant 45927, torsion ℤ/8ℤ.

last edited by David Renshaw at 2026-09-23 14:57:08 UTC · history