{
  "id": 2701,
  "curve_key": "1273873:-448032025",
  "ainvs": [
    "1",
    "0",
    "0",
    "-26539",
    "516344"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    4,
    2
  ],
  "naive_height": 42.172717272351015,
  "faltings_height": 1.576452881581764,
  "conductor": "52923",
  "bad_primes": [
    "3",
    "13",
    "23",
    "59"
  ],
  "discriminant": "1080120253623489",
  "regulator": "7.68168555371930424908414156171208264936520",
  "points": [
    [
      "5",
      "617"
    ],
    [
      "260",
      "3218"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 52923f2 = LMFDB 52923.a5: https://www.lmfdb.org/EllipticCurve/Q/52923/a/5\n\nMordell–Weil rank exactly 2 (Cremona's tables). Conductor 52923, minimal discriminant 1080120253623489, torsion ℤ/2ℤ × ℤ/4ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:18:23",
  "updated_at": "2026-09-26 20:18:23"
}