curve #3029

y² = x³ − 348x + 2497

a-invariants: [0, 0, 0, -348, 2497]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/6ℤ
conductor (N): 1260
discriminant (Δ): 3704400
Faltings height: 0.1907
naive height: 29.1702
primes of bad reduction: 2, 3, 5, 7
regulator: 1.033816853039532233941388221852962733779
submitted by: David Renshaw
submitted at: 2026-09-26 20:33:59 UTC
last updated: 2026-09-26 20:33:59 UTC

Witness: 1 independent point log in to add more points →

(6, 25)

Commentary

Cremona 1260b1 = LMFDB 1260.d4: https://www.lmfdb.org/EllipticCurve/Q/1260/d/4 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 1260, minimal discriminant 3704400, torsion ℤ/6ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:33:59 UTC · history