{
  "id": 3304,
  "curve_key": "17918241:-75847812561",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-373297",
    "87880144"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    4
  ],
  "naive_height": 50.10398940663317,
  "faltings_height": 1.5020761411378818,
  "conductor": "275665",
  "bad_primes": [
    "5",
    "13",
    "4241"
  ],
  "discriminant": "17918225",
  "regulator": "30.9837404644778331078053405938909747069624",
  "points": [
    [
      "64",
      "7983"
    ],
    [
      "4018/9",
      "79582/27"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 275665c1 = LMFDB 275665.c3: https://www.lmfdb.org/EllipticCurve/Q/275665/c/3\n\nMordell–Weil rank exactly 2 (Cremona's tables). Conductor 275665, minimal discriminant 17918225, torsion ℤ/4ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:54:40",
  "updated_at": "2026-09-26 20:54:40"
}