{
  "id": 1635,
  "curve_key": "1368185208021947995408:-50342931461308290631672875793856",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-28503858500457249904",
    "58267281793422918842366393248"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    8
  ],
  "naive_height": 146.00331644667725,
  "faltings_height": 10.004672501511465,
  "conductor": "198425172913968",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "13",
    "43",
    "53",
    "73",
    "103",
    "241"
  ],
  "discriminant": "15472935691910695297211983556109336098213182256608620705792",
  "regulator": "3417.660717931345791056081138496159216584618200",
  "points": [
    [
      "5726216868",
      "287764027979428"
    ],
    [
      "59438022649/25",
      "7844136373062132/125"
    ],
    [
      "6295038738916/2209",
      "1398936628696266660/103823"
    ],
    [
      "3927026631992743372/306845289",
      "7190619210247320361897427044/5375008927413"
    ]
  ],
  "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 02:01:19",
  "updated_at": "2026-09-25 02:01:19"
}