curve #954

y² + xy + y = x³ + x² + 5x + 9

a-invariants: [1, 1, 1, 5, 9]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/5ℤ
conductor (N): 58
discriminant (Δ): -29696
Faltings height: -0.4576
naive height: 17.4442
primes of bad reduction: 2, 29
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:05:45 UTC
last updated: 2026-09-23 15:05:45 UTC

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

Commentary

Cremona 58b1 = LMFDB 58.b2: https://www.lmfdb.org/EllipticCurve/Q/58/b/2 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 58, minimal discriminant -29696, torsion ℤ/5ℤ.

last edited by David Renshaw at 2026-09-23 15:05:45 UTC · history