{
  "id": 3042,
  "curve_key": "86670345549754576995491666607856:-809709975123792067763349278688110313553510521496",
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  "rank_lower_bound": 8,
  "torsion": [
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  "naive_height": 220.62601062575735,
  "faltings_height": 16.206822373969118,
  "conductor": "1081272252106752146999637106755",
  "bad_primes": [
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    "29",
    "31",
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    "434431",
    "31000374311"
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  "discriminant": "-2652997589211787107549609960763935271906042933101162278505560435058165717701520446152996875",
  "regulator": "4006404.58857809070596279583881531983251471294729208522",
  "points": [
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    [
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  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Dujella - Lecacheux (2009). Source: https://dujella.github.io/tors/z5old678.html (curve entry 4). Published independent points; exact point coordinates checked.",
  "created_at": "2026-09-26 20:34:36",
  "updated_at": "2026-09-26 20:34:36"
}