curve #1003

y² + xy = x³ − 115x + 392

a-invariants: [1, 0, 0, -115, 392]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 195
discriminant (Δ): 27720225
Faltings height: 0.1497
naive height: 25.8489
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 195a2 = LMFDB 195.a5: https://www.lmfdb.org/EllipticCurve/Q/195/a/5 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 195, minimal discriminant 27720225, torsion ℤ/2ℤ × ℤ/4ℤ.

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