curve #2705

y² = x³ − x² − 42964x + 3440644

a-invariants: [0, -1, 0, -42964, 3440644]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 54264
discriminant (Δ): 4251975969024
Faltings height: 1.3774
naive height: 43.6180
primes of bad reduction: 2, 3, 7, 17, 19
regulator: 4.52326842104789240261453743697340266823019
submitted by: David Renshaw
submitted at: 2026-09-26 20:18:33 UTC
last updated: 2026-09-26 20:18:33 UTC

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

(104, 294)
(124, 66)

Commentary

Cremona 54264h2 = LMFDB 54264.b3: https://www.lmfdb.org/EllipticCurve/Q/54264/b/3 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 54264, minimal discriminant 4251975969024, torsion ℤ/2ℤ × ℤ/4ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:18:33 UTC · history