curve #3018

y² + xy + y = x³ − 58x + 56

a-invariants: [1, 0, 1, -58, 56]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/6ℤ
conductor (N): 870
discriminant (Δ): 10570500
Faltings height: 0.0405
naive height: 23.7700
primes of bad reduction: 2, 3, 5, 29
regulator: 0.9922518400487123482261270061277082571301
submitted by: David Renshaw
submitted at: 2026-09-26 20:33:31 UTC
last updated: 2026-09-26 20:33:31 UTC

Witness: 1 independent point log in to add more points →

(0, 7)

Commentary

Cremona 870c1 = LMFDB 870.c3: https://www.lmfdb.org/EllipticCurve/Q/870/c/3 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 870, minimal discriminant 10570500, torsion ℤ/6ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:33:31 UTC · history