{
  "id": 3326,
  "curve_key": "9080665:-27363803869",
  "ainvs": [
    "1",
    "0",
    "1",
    "-189181",
    "31655304"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    6
  ],
  "naive_height": 48.064973957343526,
  "faltings_height": 1.494525590809702,
  "conductor": "84058",
  "bad_primes": [
    "2",
    "13",
    "53",
    "61"
  ],
  "discriminant": "24556367888",
  "regulator": "15.8652895402759803982128151088805353141043",
  "points": [
    [
      "459",
      "6218"
    ],
    [
      "-386",
      "7063"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 84058j1 = LMFDB 84058.a2: https://www.lmfdb.org/EllipticCurve/Q/84058/a/2\n\nMordell–Weil rank exactly 2 (Cremona's tables). Conductor 84058, minimal discriminant 24556367888, torsion ℤ/6ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:58:14",
  "updated_at": "2026-09-26 20:58:14"
}