{
  "id": 1569,
  "curve_key": "3672473537296:-23867835654420011456",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-76509865360",
    "27624835288496800"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    8
  ],
  "naive_height": 89.23812687585126,
  "faltings_height": 5.491389341083934,
  "conductor": "676608240",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "19",
    "41",
    "47"
  ],
  "discriminant": "-301008507504845269801122088394803200",
  "regulator": "188.10011583802142472399808927788575718725849",
  "points": [
    [
      "2440722",
      "3792171262"
    ],
    [
      "1601603930/961",
      "63400933225410/29791"
    ],
    [
      "2725409641/2025",
      "140065216373764/91125"
    ]
  ],
  "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 01:13:19",
  "updated_at": "2026-09-25 01:13:19"
}