{
  "id": 1319,
  "curve_key": "8192236710217:-21512634570703495621",
  "ainvs": [
    "1",
    "0",
    "1",
    "-170671598130",
    "24898868382347720"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    3
  ],
  "naive_height": 89.2026242372952,
  "faltings_height": 5.397769179330956,
  "conductor": "21257773462978",
  "bad_primes": [
    "2",
    "13",
    "19",
    "31",
    "83",
    "103",
    "397",
    "409"
  ],
  "discriminant": "50353023815799767963666602409522924",
  "regulator": "3914.2779940292363748020915176307803194473405753398",
  "points": [
    [
      "3453323",
      "6371491759"
    ],
    [
      "154027",
      "47515269"
    ],
    [
      "682760",
      "475733695"
    ],
    [
      "86495120/289",
      "122329965160/4913"
    ],
    [
      "1158136177/1024",
      "37033554373881/32768"
    ],
    [
      "38812605",
      "241768558195"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Torsion Z/3. From Michael Rubinstein's github repository:\nhttps://github.com/mrubinst/elliptic-curves-by-rank",
  "created_at": "2026-09-24 17:31:27",
  "updated_at": "2026-09-24 17:31:27"
}