curve #3271

y² = x³ − x² − 107460x − 10755900

a-invariants: [0, -1, 0, -107460, -10755900]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 62040
discriminant (Δ): 29107772100000000
Faltings height: 1.8737
naive height: 46.3682
primes of bad reduction: 2, 3, 5, 11, 47
regulator: 4.36782012405061090810557903857322414456116
submitted by: David Renshaw
submitted at: 2026-09-26 20:49:19 UTC
last updated: 2026-09-26 20:49:19 UTC

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

(450, 5640)
(-120, 630)

Commentary

Cremona 62040s2 = LMFDB 62040.i4: https://www.lmfdb.org/EllipticCurve/Q/62040/i/4 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 62040, minimal discriminant 29107772100000000, torsion ℤ/2ℤ × ℤ/4ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:49:20 UTC · history