{
  "id": 2931,
  "curve_key": "48856480911692154826646161:-504573522667312696858885012323366102841",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1017843352326919892221795",
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  ],
  "rank_lower_bound": 7,
  "torsion": [
    5
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  "naive_height": 178.23355382138445,
  "faltings_height": 12.880917202156702,
  "conductor": "1856561926508441474869470",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "17",
    "23",
    "37",
    "47",
    "73",
    "16481",
    "982459601"
  ],
  "discriminant": "-79847328043998607095435278135800408772374744064751415262723013005414400000",
  "regulator": "115262.6674560557768376904929488470510685063604784333",
  "points": [
    [
      "60009577390",
      "723279229166022505"
    ],
    [
      "509759245670",
      "444527923405600505"
    ],
    [
      "-121890379090",
      "-840387639572936215"
    ],
    [
      "207429320080",
      "617892786310079905"
    ],
    [
      "320127896840",
      "539410987983979505"
    ],
    [
      "-384838786210",
      "-958492251841957495"
    ],
    [
      "704156584190",
      "465212037243711305"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Dujella - Lecacheux (2009). Source: https://dujella.github.io/tors/z5old678.html (curve entry 24). Published independent points; exact point coordinates checked.",
  "created_at": "2026-09-26 20:28:54",
  "updated_at": "2026-09-26 20:28:54"
}