{
  "id": 1653,
  "curve_key": "199734129025:-89250994864678625",
  "ainvs": [
    "1",
    "1",
    "1",
    "-4161127688",
    "103298028771656"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    4
  ],
  "naive_height": 78.0607588927302,
  "faltings_height": 4.213658138170544,
  "conductor": "84289510725",
  "bad_primes": [
    "3",
    "5",
    "7",
    "31",
    "41",
    "59",
    "2141"
  ],
  "discriminant": "1387611282752763473214140625",
  "regulator": "291.949263499520059760810575449623252151716349184",
  "points": [
    [
      "42420",
      "-1787048"
    ],
    [
      "-32005",
      "-14256098"
    ],
    [
      "17328045/16",
      "71971656403/64"
    ],
    [
      "36840",
      "31567"
    ],
    [
      "36096",
      "-378377"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Torsion Z/4. From Michael Rubinstein's github repository:\nhttps://github.com/mrubinst/elliptic-curves-by-rank",
  "created_at": "2026-09-25 02:28:26",
  "updated_at": "2026-09-25 02:28:26"
}