{
  "id": 3014,
  "curve_key": "247120:-415534040",
  "ainvs": [
    "0",
    "-1",
    "1",
    "-5148",
    "482658"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    5
  ],
  "naive_height": 39.690150188590344,
  "faltings_height": 1.3623694022975716,
  "conductor": "218075",
  "bad_primes": [
    "5",
    "11",
    "13",
    "61"
  ],
  "discriminant": "-91190591138075",
  "regulator": "9.05842331896709286253696894846352702307362",
  "points": [
    [
      "-99",
      "110"
    ],
    [
      "118",
      "1226"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 218075b1 = LMFDB 218075.b2: https://www.lmfdb.org/EllipticCurve/Q/218075/b/2\n\nMordell–Weil rank exactly 2 (Cremona's tables). Conductor 218075, minimal discriminant -91190591138075, torsion ℤ/5ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:33:20",
  "updated_at": "2026-09-26 20:33:20"
}