{
  "id": 4045,
  "curve_key": "2181702793:-99317693943845",
  "ainvs": [
    "1",
    "1",
    "0",
    "-45452141",
    "114932096265"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    2
  ],
  "naive_height": 64.51011451966733,
  "faltings_height": 3.2829813454541754,
  "conductor": "26676134520303198",
  "bad_primes": [
    "2",
    "3",
    "7",
    "29",
    "73",
    "127",
    "457",
    "673",
    "7681"
  ],
  "discriminant": "301228991741756295465444",
  "regulator": "20790.5488616135501395074021144322586615712885975128218",
  "points": [
    [
      "-860",
      "392075"
    ],
    [
      "4907",
      "97958"
    ],
    [
      "8708",
      "611723"
    ],
    [
      "-30961/4",
      "475531/8"
    ],
    [
      "4592",
      "53123"
    ],
    [
      "18193",
      "2295258"
    ],
    [
      "-309",
      "359247"
    ],
    [
      "5152",
      "-135037"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Torsion Z/2. From Michael Rubinstein's github repository:\nhttps://github.com/mrubinst/elliptic-curves-by-rank",
  "created_at": "2026-10-07 22:22:14",
  "updated_at": "2026-10-07 22:22:14"
}