{
  "id": 2807,
  "curve_key": "8578235738411823939061293046589041:-24319755316332341239498857431049754273151445869585161",
  "ainvs": [
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  "rank_lower_bound": 4,
  "torsion": [
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  "naive_height": 241.2462574774752,
  "faltings_height": 18.161628924063223,
  "conductor": "28352480766588873916770",
  "bad_primes": [
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    "3",
    "5",
    "7",
    "17",
    "31",
    "37",
    "41",
    "71",
    "3433",
    "4481",
    "154621"
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  "discriminant": "-341909293686297566077998559177502779659929245706014307451860138993072903043647112803442229248000000000",
  "regulator": "195914.5087681290415403782302971061364423143486",
  "points": [
    [
      "101629293809588610",
      "32552494216369407363685695"
    ],
    [
      "-15202948761734070",
      "-5229816529060178755649625"
    ],
    [
      "17334183174096114397199346/271227961",
      "74445992775872903454362900009494808403/4466853289709"
    ],
    [
      "862411646113780429977408418/151606660689",
      "308518103427511192437597862833954996411673/59030630652493863"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "van Beek (2015). Source: https://dujella.github.io/tors/z9.html (curve entry 3). Published independent points; exact point coordinates checked.",
  "created_at": "2026-09-26 20:23:18",
  "updated_at": "2026-09-26 20:23:18"
}