{
  "id": 3288,
  "curve_key": "23056:-3500864",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-480",
    "4212"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    4
  ],
  "naive_height": 30.13704395471791,
  "faltings_height": 0.09231944093480156,
  "conductor": "480",
  "bad_primes": [
    "2",
    "3",
    "5"
  ],
  "discriminant": "23040",
  "regulator": "2.065113879773876953777854130157768173856",
  "points": [
    [
      "17",
      "26"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 480f3 = LMFDB 480.c1: https://www.lmfdb.org/EllipticCurve/Q/480/c/1\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 480, minimal discriminant 23040, torsion ℤ/4ℤ. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-26 20:52:05",
  "updated_at": "2026-09-26 20:52:05"
}