{
  "id": 3048,
  "curve_key": "41610871317617448180659524113616:-52894714229626940143693482729186653610614761664",
  "ainvs": [
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  "rank_lower_bound": 8,
  "torsion": [
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  "naive_height": 218.41774275809502,
  "faltings_height": 16.267316698822896,
  "conductor": "1706951126476128669388929683160",
  "bad_primes": [
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    "73",
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    "223",
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  "discriminant": "40075173819244977063109444068398435816801715759648817230455414830191768100293683644217760000",
  "regulator": "1290756.44416902203971720599214457641890155388609825901",
  "points": [
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      "4806685314955215492570"
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    [
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    [
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    [
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    [
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  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Dujella - Eroshkin (2008). Source: https://dujella.github.io/tors/z2z4old678.html (curve entry 4). Published independent points; exact point coordinates checked.",
  "created_at": "2026-09-26 20:34:51",
  "updated_at": "2026-09-26 20:34:51"
}