curve #1004

y² + xy = x³ − 520x − 4225

a-invariants: [1, 0, 0, -520, -4225]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 195
discriminant (Δ): 1445900625
Faltings height: 0.4963
naive height: 30.3752
primes of bad reduction: 3, 5, 13
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:13:18 UTC
last updated: 2026-09-23 15:13:18 UTC

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Commentary

Cremona 195a3 = LMFDB 195.a4: https://www.lmfdb.org/EllipticCurve/Q/195/a/4 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 195, minimal discriminant 1445900625, torsion ℤ/2ℤ × ℤ/4ℤ.

last edited by David Renshaw at 2026-09-23 15:13:18 UTC · history