curve #2889

y² = x³ − x² − 310x + 2200

a-invariants: [0, -1, 0, -310, 2200]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 14880
discriminant (Δ): 13838400
Faltings height: 0.2250
naive height: 28.8265
primes of bad reduction: 2, 3, 5, 31
regulator: 2.52781196784898510318028881762336153542262
submitted by: David Renshaw
submitted at: 2026-09-26 20:27:01 UTC
last updated: 2026-09-26 20:27:01 UTC

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

(12, 8)
(7, 18)

Commentary

Cremona 14880l1 = LMFDB 14880.c3: https://www.lmfdb.org/EllipticCurve/Q/14880/c/3 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 14880, minimal discriminant 13838400, torsion ℤ/2ℤ × ℤ/2ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:27:01 UTC · history