{
  "id": 2820,
  "curve_key": "946585:-920958013",
  "ainvs": [
    "1",
    "0",
    "1",
    "-19721",
    "1064280"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    3
  ],
  "naive_height": 41.28185000937925,
  "faltings_height": 1.0073526194291769,
  "conductor": "474734",
  "bad_primes": [
    "2",
    "13",
    "19",
    "31"
  ],
  "discriminant": "-912438748",
  "regulator": "12.966359339984050889460103345345901338633648",
  "points": [
    [
      "49",
      "440"
    ],
    [
      "85",
      "20"
    ],
    [
      "36",
      "615"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 474734e1 = LMFDB 474734.e1: https://www.lmfdb.org/EllipticCurve/Q/474734/e/1\n\nMordell–Weil rank exactly 3 (Cremona's tables). Conductor 474734, minimal discriminant -912438748, torsion ℤ/3ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:23:55",
  "updated_at": "2026-09-26 20:23:55"
}