{
  "id": 2971,
  "curve_key": "7099153:-18856168345",
  "ainvs": [
    "1",
    "0",
    "0",
    "-147899",
    "21811944"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    4,
    2
  ],
  "naive_height": 47.32645811736177,
  "faltings_height": 1.7606163887443254,
  "conductor": "102297",
  "bad_primes": [
    "3",
    "13",
    "43",
    "61"
  ],
  "discriminant": "1289258573625009",
  "regulator": "7.89215400433262179791218735151313604685613",
  "points": [
    [
      "244",
      "394"
    ],
    [
      "-57",
      "5511"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 102297f2 = LMFDB 102297.d4: https://www.lmfdb.org/EllipticCurve/Q/102297/d/4\n\nMordell–Weil rank exactly 2 (Cremona's tables). Conductor 102297, minimal discriminant 1289258573625009, torsion ℤ/2ℤ × ℤ/4ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:31:05",
  "updated_at": "2026-09-26 20:31:05"
}