curve #969

y² + y = x³ + x² + 2x + 4

a-invariants: [0, 1, 1, 2, 4]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/5ℤ
conductor (N): 75
discriminant (Δ): -6075
Faltings height: -0.5931
naive height: 16.1167
primes of bad reduction: 3, 5
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:07:55 UTC
last updated: 2026-09-23 15:07:55 UTC

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Commentary

Cremona 75c1 = LMFDB 75.a2: https://www.lmfdb.org/EllipticCurve/Q/75/a/2 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 75, minimal discriminant -6075, torsion ℤ/5ℤ.

last edited by David Renshaw at 2026-09-23 15:07:55 UTC · history