{
  "id": 3305,
  "curve_key": "20222961:-90942547689",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-421312",
    "105362906"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    4
  ],
  "naive_height": 50.46698760001371,
  "faltings_height": 1.5287166032783612,
  "conductor": "301835",
  "bad_primes": [
    "5",
    "17",
    "53",
    "67"
  ],
  "discriminant": "20222945",
  "regulator": "75.0449208322522443392470236208540186280691",
  "points": [
    [
      "-2725/4",
      "72401/8"
    ],
    [
      "226504/225",
      "87635903/3375"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 301835b1 = LMFDB 301835.b3: https://www.lmfdb.org/EllipticCurve/Q/301835/b/3\n\nMordell–Weil rank exactly 2 (Cremona's tables). Conductor 301835, minimal discriminant 20222945, torsion ℤ/4ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:54:50",
  "updated_at": "2026-09-26 20:54:50"
}