{
  "id": 2908,
  "curve_key": "2165937709230771932132361:1696494967281921692769142929905768859",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-45123702275641081919424",
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  ],
  "rank_lower_bound": 7,
  "torsion": [
    6
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  "naive_height": 168.10468686476344,
  "faltings_height": 12.056994018898106,
  "conductor": "407739781740207625175610",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "17",
    "19",
    "29",
    "41",
    "67",
    "101",
    "997",
    "2141",
    "5711"
  ],
  "discriminant": "4214663440569253095228975629561450754700660667382890675014820877562500",
  "regulator": "477043.0331294476419166005689599831646627442411355343",
  "points": [
    [
      "-46184748668",
      "-4687994158267666"
    ],
    [
      "-60161183646",
      "-23095727833899384"
    ],
    [
      "-48542581178",
      "-10606589957382016"
    ],
    [
      "-55854944093",
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    ],
    [
      "-185253203193",
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    ],
    [
      "-64106657393",
      "-25801849446340566"
    ],
    [
      "-45896523588",
      "-3287014604709246"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Dujella (2001). Source: https://dujella.github.io/tors/z6old678.html (curve entry 122). Published independent points; exact point coordinates checked.",
  "created_at": "2026-09-26 20:27:52",
  "updated_at": "2026-09-26 20:27:52"
}