curve #2954

y² = x³ + 225

a-invariants: [0, 0, 0, 0, 225]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/3ℤ
conductor (N): 24300
discriminant (Δ): -21870000
Faltings height: 0.0873
naive height: 24.3553
primes of bad reduction: 2, 3, 5
regulator: 1.38909303935706191886763522495118242671012
submitted by: David Renshaw
submitted at: 2026-09-26 20:29:57 UTC
last updated: 2026-09-26 20:29:57 UTC

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

(-6, 3)
(6, 21)

Commentary

Cremona 24300x1 = LMFDB 24300.e2: https://www.lmfdb.org/EllipticCurve/Q/24300/e/2 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 24300, minimal discriminant -21870000, torsion ℤ/3ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:29:57 UTC · history