{
  "id": 2896,
  "curve_key": "12208:-1295360",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-254",
    "1584"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    2,
    2
  ],
  "naive_height": 28.229540260572715,
  "faltings_height": 0.28072897946068104,
  "conductor": "36192",
  "bad_primes": [
    "2",
    "3",
    "13",
    "29"
  ],
  "discriminant": "81866304",
  "regulator": "3.19828276400573861070694160566871278007081",
  "points": [
    [
      "-5",
      "52"
    ],
    [
      "7",
      "10"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 36192j1 = LMFDB 36192.c3: https://www.lmfdb.org/EllipticCurve/Q/36192/c/3\n\nMordell–Weil rank exactly 2 (Cremona's tables). Conductor 36192, minimal discriminant 81866304, torsion ℤ/2ℤ × ℤ/2ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:27:19",
  "updated_at": "2026-09-26 20:27:19"
}