{
  "id": 3451,
  "curve_key": "769746537:-21496145360949",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-16036386",
    "24883806968"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    3
  ],
  "naive_height": 61.397789498902675,
  "faltings_height": 2.9632431484797936,
  "conductor": "18135416754",
  "bad_primes": [
    "2",
    "3",
    "7",
    "13",
    "43",
    "61",
    "67"
  ],
  "discriminant": "-3473351638290040168116",
  "regulator": "76.5906563404152064607757282615977538600697382928",
  "points": [
    [
      "26323",
      "4210753"
    ],
    [
      "-57011/16",
      "12387283/64"
    ],
    [
      "14062",
      "1599160"
    ],
    [
      "193",
      "147538"
    ],
    [
      "73634/25",
      "6882338/125"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Torsion Z/3. From Michael Rubinstein's github repository:\nhttps://github.com/mrubinst/elliptic-curves-by-rank",
  "created_at": "2026-09-27 05:35:52",
  "updated_at": "2026-09-27 05:35:52"
}