curve #898

y² + xy = x³ − 34x − 217

a-invariants: [1, 0, 0, -34, -217]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/2ℤ
conductor (N): 21
discriminant (Δ): -17294403
Faltings height: 0.0742
naive height: 24.2566
primes of bad reduction: 3, 7
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 14:57:10 UTC
last updated: 2026-09-23 14:57:10 UTC

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Commentary

Cremona 21a6 = LMFDB 21.a4: https://www.lmfdb.org/EllipticCurve/Q/21/a/4 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 21, minimal discriminant -17294403, torsion ℤ/2ℤ.

last edited by David Renshaw at 2026-09-23 14:57:10 UTC · history