curve #3036

y² + xy + y = x³ − 6329x + 166152

a-invariants: [1, 0, 1, -6329, 166152]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/6ℤ
conductor (N): 86870
discriminant (Δ): 4219469620100
Faltings height: 1.1467
naive height: 37.8721
primes of bad reduction: 2, 5, 7, 17, 73
regulator: 3.55147210464094012170507548866403183375687
submitted by: David Renshaw
submitted at: 2026-09-26 20:34:19 UTC
last updated: 2026-09-26 20:34:19 UTC

Witness: 2 independent points log in to add more points →

(29, 70)
(63, 104)

Commentary

Cremona 86870g1 = LMFDB 86870.b3: https://www.lmfdb.org/EllipticCurve/Q/86870/b/3 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 86870, minimal discriminant 4219469620100, torsion ℤ/6ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:34:19 UTC · history