{
  "id": 3320,
  "curve_key": "-536231:-253865053",
  "ainvs": [
    "1",
    "0",
    "1",
    "11171",
    "294756"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    6
  ],
  "naive_height": 39.576960952083695,
  "faltings_height": 1.3937338499343574,
  "conductor": "41230",
  "bad_primes": [
    "2",
    "5",
    "7",
    "19",
    "31"
  ],
  "discriminant": "-126526217059900",
  "regulator": "2.83540656752120477709686561017778208536915",
  "points": [
    [
      "-7",
      "468"
    ],
    [
      "13",
      "658"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 41230k1 = LMFDB 41230.b4: https://www.lmfdb.org/EllipticCurve/Q/41230/b/4\n\nMordell–Weil rank exactly 2 (Cremona's tables). Conductor 41230, minimal discriminant -126526217059900, torsion ℤ/6ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:57:15",
  "updated_at": "2026-09-26 20:57:15"
}