{
  "id": 2829,
  "curve_key": "568782459434438336051666297506576:-13490290294905495801918695629391791604554365770176",
  "ainvs": [
    "0",
    "1",
    "0",
    "-11849634571550798667743047864720",
    "15613761915399875450490670165233536220551598068"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    8
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  "naive_height": 226.26315248997327,
  "faltings_height": 16.69509762072985,
  "conductor": "268219200835595648336880",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "19",
    "29",
    "31",
    "43",
    "53",
    "71",
    "109",
    "5393",
    "7559"
  ],
  "discriminant": "1169481526410074053786922482309278316219381732805207421351270588339386470611845324037600000000",
  "regulator": "141747.883076332150560403017089580086904045519139",
  "points": [
    [
      "1408739633544836",
      "41429730450937797313410"
    ],
    [
      "-218498788069669",
      "134879432087724391611000"
    ],
    [
      "740396620160686",
      "85124664142477399663860"
    ],
    [
      "1278614340522956",
      "50527198607648165081250"
    ],
    [
      "1650944116469206",
      "23463118324372658662500"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Dujella - Lecacheux (2002). Source: https://dujella.github.io/tors/z8old5.html (curve entry 1). Published independent points; exact point coordinates checked.",
  "created_at": "2026-09-26 20:24:18",
  "updated_at": "2026-09-26 20:24:18"
}