curve #3014

y² + y = x³ − x² − 5148x + 482658

a-invariants: [0, -1, 1, -5148, 482658]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/5ℤ
conductor (N): 218075
discriminant (Δ): -91190591138075
Faltings height: 1.3624
naive height: 39.6902
primes of bad reduction: 5, 11, 13, 61
regulator: 9.05842331896709286253696894846352702307362
submitted by: David Renshaw
submitted at: 2026-09-26 20:33:20 UTC
last updated: 2026-09-26 20:33:20 UTC

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

(-99, 110)
(118, 1226)

Commentary

Cremona 218075b1 = LMFDB 218075.b2: https://www.lmfdb.org/EllipticCurve/Q/218075/b/2 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 218075, minimal discriminant -91190591138075, torsion ℤ/5ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:33:21 UTC · history