curve #964

y² + xy = x³ + 115x + 561

a-invariants: [1, 0, 0, 115, 561]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/10ℤ
conductor (N): 66 ☆ record for ℤ/10ℤ torsion, rank ≥ 0
discriminant (Δ): -228637728
Faltings height: 0.2897
naive height: 26.1481
primes of bad reduction: 2, 3, 11
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:07:52 UTC
last updated: 2026-09-23 15:07:52 UTC

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Commentary

Cremona 66c2 = LMFDB 66.c4: https://www.lmfdb.org/EllipticCurve/Q/66/c/4 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 66, minimal discriminant -228637728, torsion ℤ/10ℤ.

last edited by David Renshaw at 2026-09-23 15:07:53 UTC · history