curve #3310

y² + y = x³ + x² − 174580x + 28018120

a-invariants: [0, 1, 1, -174580, 28018120]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/5ℤ
conductor (N): 149397
discriminant (Δ): 1577034881397
Faltings height: 1.5751
naive height: 47.8240
primes of bad reduction: 3, 19, 2621
regulator: 7.57698998751365494134199839839698678044952
submitted by: David Renshaw
submitted at: 2026-09-26 20:55:39 UTC
last updated: 2026-09-26 20:55:39 UTC

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

(254, 355)
(260, 520)

Commentary

Cremona 149397a1 = LMFDB 149397.b2: https://www.lmfdb.org/EllipticCurve/Q/149397/b/2 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 149397, minimal discriminant 1577034881397, torsion ℤ/5ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:55:39 UTC · history