{
  "id": 1638,
  "curve_key": "4560458224538034138433:210556849692567589132901706024479",
  "ainvs": [
    "1",
    "0",
    "0",
    "-95009546344542377884",
    "-243700057522463282951051802352"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    8
  ],
  "naive_height": 149.61513017756994,
  "faltings_height": 10.498826678706942,
  "conductor": "469844835723354",
  "bad_primes": [
    "2",
    "3",
    "7",
    "13",
    "23",
    "29",
    "31",
    "41",
    "1015057"
  ],
  "discriminant": "29232185378058901666647063249511076348229020704652247309484032",
  "regulator": "1432.171744928611192031193225914770310965011620",
  "points": [
    [
      "116265280922",
      "39501072957731126"
    ],
    [
      "-6525926344",
      "313692527940260"
    ],
    [
      "-6610314172",
      "309029080302824"
    ],
    [
      "727888588338296/44521",
      "15068749461867266264204/9393931"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Torsion Z/8. From Michael Rubinstein's github repository:\nhttps://github.com/mrubinst/elliptic-curves-by-rank",
  "created_at": "2026-09-25 02:07:19",
  "updated_at": "2026-09-25 02:07:19"
}