{
  "id": 1339,
  "curve_key": "112609144809:-10783047019795839477",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-2346023850",
    "12480379081640036"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    3
  ],
  "naive_height": 87.64901370866376,
  "faltings_height": 5.361749477382752,
  "conductor": "33696840882516030",
  "bad_primes": [
    "2",
    "3",
    "5",
    "37",
    "53",
    "61",
    "163",
    "233",
    "9157"
  ],
  "discriminant": "-67287427693801602746701454437978800",
  "regulator": "18335.26638309335522512868752126847470019477195770176",
  "points": [
    [
      "639323",
      "521497536"
    ],
    [
      "-77552",
      "110473786"
    ],
    [
      "-51797",
      "111663376"
    ],
    [
      "3198428",
      "5718951546"
    ],
    [
      "-135272",
      "101667046"
    ],
    [
      "-235172",
      "5183626"
    ],
    [
      "688348",
      "-580878614"
    ]
  ],
  "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 17:34:52",
  "updated_at": "2026-09-24 17:34:52"
}