{
  "id": 3028,
  "curve_key": "21754581811731889990819586590878016:-3208677795402775306476114537983306875773080657268064",
  "ainvs": [
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  "rank_lower_bound": 8,
  "torsion": [
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  "naive_height": 237.19539738649073,
  "faltings_height": 17.104182264710243,
  "conductor": "31602563084617300276824095632860",
  "bad_primes": [
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    "13",
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    "29",
    "37",
    "79",
    "109",
    "127",
    "233",
    "3613",
    "6659",
    "3477917"
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  "discriminant": "67008919404042181171177088715917552997924897283354170042932893816038021962155357655250000",
  "regulator": "34331805.7328147433758740668499614526968975760832394168",
  "points": [
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      "7897185698712315",
      "791892431774850716925615"
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    [
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      "2640456633311322595662375"
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    [
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    [
      "1355808910864875",
      "1761181248419137157468625"
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  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Dujella - Peral - Tadic (2019). Source: https://dujella.github.io/tors/z6old678.html (curve entry 27). Published independent points; exact point coordinates checked.",
  "created_at": "2026-09-26 20:33:59",
  "updated_at": "2026-09-26 20:33:59"
}