{
  "id": 3040,
  "curve_key": "152089:-182598013",
  "ainvs": [
    "1",
    "0",
    "1",
    "-3169",
    "211076"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    6
  ],
  "naive_height": 38.045595288714566,
  "faltings_height": 1.2244233412134646,
  "conductor": "20130",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "61"
  ],
  "discriminant": "-17259290492400",
  "regulator": "2.38440484978054775239540980049951444880656",
  "points": [
    [
      "31",
      "362"
    ],
    [
      "70",
      "542"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 20130g1 = LMFDB 20130.e3: https://www.lmfdb.org/EllipticCurve/Q/20130/e/3\n\nMordell–Weil rank exactly 2 (Cremona's tables). Conductor 20130, minimal discriminant -17259290492400, torsion ℤ/6ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:34:29",
  "updated_at": "2026-09-26 20:34:29"
}