{
  "id": 5168,
  "curve_key": "2688:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-56",
    "0"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    2
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  "family": null,
  "families": [
    "quartic"
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  "naive_height": 23.68965810492912,
  "faltings_height": 0.04237858705225044,
  "conductor": "12544",
  "bad_primes": [
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    "7"
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  "discriminant": "11239424",
  "regulator": "11.8698271937727356034359746129077807201189",
  "points": [
    [
      "9",
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    ],
    [
      "169/9",
      "2015/27"
    ]
  ],
  "submitter": "hdeping",
  "history": [],
  "commentary": null,
  "created_at": "2026-10-21 06:44:43",
  "updated_at": "2026-10-21 06:44:43"
}