{
  "id": 3459,
  "curve_key": "657304415626537:-16840803914255689224661",
  "ainvs": [
    "1",
    "0",
    "1",
    "-13693841992220",
    "19491670055901696510"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    3
  ],
  "naive_height": 102.3575051070023,
  "faltings_height": 6.288300707238138,
  "conductor": "72865681816774464982",
  "bad_primes": [
    "2",
    "7",
    "13",
    "83",
    "349",
    "463",
    "661",
    "2137",
    "3019"
  ],
  "discriminant": "217072513013507699543036794738086818444",
  "regulator": "249175.778408709601909537243660545239186280848175959299",
  "points": [
    [
      "-3924703",
      "-3573311611"
    ],
    [
      "-1016137",
      "5688855229"
    ],
    [
      "19862385",
      "87073333985"
    ],
    [
      "10716283",
      "33211939307"
    ],
    [
      "2082259",
      "-77259727"
    ],
    [
      "-4117311",
      "2466971573"
    ],
    [
      "976207587/484",
      "-2965313601639/10648"
    ],
    [
      "-537075360/169",
      "12219000475170/2197"
    ]
  ],
  "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 05:39:06",
  "updated_at": "2026-09-27 05:39:06"
}