{
  "id": 1356,
  "curve_key": "12968561868801721:-1478933589223451606743981",
  "ainvs": [
    "1",
    "0",
    "1",
    "-270178372266703",
    "1711728668715982411506"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    3
  ],
  "naive_height": 111.30672702418356,
  "faltings_height": 7.061557472398773,
  "conductor": "18634368691081768030",
  "bad_primes": [
    "2",
    "5",
    "7",
    "37",
    "59",
    "79",
    "103",
    "109",
    "367",
    "491"
  ],
  "discriminant": "-3556237867662447616318234077025105468750000",
  "regulator": "175336.693154936057489668009485700817138591305175743545",
  "points": [
    [
      "10371555",
      "5016590372"
    ],
    [
      "7474655",
      "10477246872"
    ],
    [
      "-19868330/9",
      "-1294116481456/27"
    ],
    [
      "2044195",
      "34174605732"
    ],
    [
      "758873945/64",
      "6774777910839/512"
    ],
    [
      "84493720/9",
      "44239841419/27"
    ],
    [
      "-8659605",
      "58330941572"
    ],
    [
      "134938255",
      "-1556426994128"
    ]
  ],
  "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 17:37:50",
  "updated_at": "2026-09-24 17:37:50"
}