{
  "id": 3119,
  "curve_key": "1456:-53504",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-30",
    "72"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    2,
    2
  ],
  "naive_height": 21.850344686269892,
  "faltings_height": -0.2542541493451711,
  "conductor": "480",
  "bad_primes": [
    "2",
    "3",
    "5"
  ],
  "discriminant": "129600",
  "regulator": "1.032556939886938476888927065078884086928",
  "points": [
    [
      "2",
      "4"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 480f1 = LMFDB 480.c3: https://www.lmfdb.org/EllipticCurve/Q/480/c/3\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 480, minimal discriminant 129600, torsion ℤ/2ℤ × ℤ/2ℤ. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-26 20:38:12",
  "updated_at": "2026-09-26 20:38:12"
}