curve #3330

y² + xy + y = x³ − 589039x + 173956686

a-invariants: [1, 0, 1, -589039, 173956686]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/6ℤ
conductor (N): 392630
discriminant (Δ): 138547348100
Faltings height: 1.7449
naive height: 51.4723
primes of bad reduction: 2, 5, 7, 71, 79
regulator: 11.0288622414088101401665668814870551477974
submitted by: David Renshaw
submitted at: 2026-09-26 20:58:53 UTC
last updated: 2026-09-26 20:58:53 UTC

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

(436, 37)
(219, 7338)

Commentary

Cremona 392630a1 = LMFDB 392630.a2: https://www.lmfdb.org/EllipticCurve/Q/392630/a/2 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 392630, minimal discriminant 138547348100, torsion ℤ/6ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:58:53 UTC · history