{
  "id": 2848,
  "curve_key": "8469012773604274348465364208001:-24645687586482237930206356724392389283061352001",
  "ainvs": [
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    "0",
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    "28525101373243316234591662405070447436360000"
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  "rank_lower_bound": 5,
  "torsion": [
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  "naive_height": 213.64190020811233,
  "faltings_height": 15.449645789257247,
  "conductor": "286506236810100584130",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "19",
    "31",
    "41",
    "347",
    "3001",
    "4049",
    "13399"
  ],
  "discriminant": "13343531912768895289323777036487063158707882858277501774785059103095699266678284640000",
  "regulator": "674378.759178133690327059763816189870983279655587",
  "points": [
    [
      "117266065309906",
      "3073679029875028041172"
    ],
    [
      "241555047802000",
      "11200344991211074600"
    ],
    [
      "219009368530500",
      "623205042126650982900"
    ],
    [
      "8985470043234687970/38809",
      "2240578986357384258280099460/7645373"
    ],
    [
      "4073801710059160",
      "258685128952480127236240"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Dujella - Kazalicki - Peral (2021). Source: https://dujella.github.io/tors/z8old5.html (curve entry 46). Published independent points; exact point coordinates checked.",
  "created_at": "2026-09-26 20:25:11",
  "updated_at": "2026-09-26 20:25:11"
}