curve #1056

y² + xy = x³ − 1480x + 94400

a-invariants: [1, 0, 0, -1480, 94400]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/7ℤ
conductor (N): 5010
discriminant (Δ): -3652290000000
Faltings height: 1.0927
naive height: 36.4363
primes of bad reduction: 2, 3, 5, 167
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:21:52 UTC
last updated: 2026-09-23 15:21:52 UTC

Witness: no points (rank ≥ 0 needs none) log in to add more points →

Commentary

Cremona 5010h1 = LMFDB 5010.h2: https://www.lmfdb.org/EllipticCurve/Q/5010/h/2 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 5010, minimal discriminant -3652290000000, torsion ℤ/7ℤ.

last edited by David Renshaw at 2026-09-23 15:21:52 UTC · history