{
  "id": 2924,
  "curve_key": "13393014540539881941426503761:-1549486401347579065293495016673733298881241",
  "ainvs": [
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    "0",
    "0",
    "-279021136261247540446385495",
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  "rank_lower_bound": 7,
  "torsion": [
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  "naive_height": 194.29359233677707,
  "faltings_height": 13.922246760521428,
  "conductor": "68510733689193262725648390",
  "bad_primes": [
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    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "19",
    "37",
    "41",
    "53",
    "79",
    "1229",
    "904816141"
  ],
  "discriminant": "830397002991485860541600591071614243527727105302650873541190745681163059200000",
  "regulator": "159006.2506431748505432562568007566739562767276232925",
  "points": [
    [
      "-5948999789450",
      "-56945102666568630155"
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    [
      "4319183174680",
      "25861542387494115115"
    ],
    [
      "-7446369281978",
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    [
      "9786751791190",
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    [
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    [
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      "1123837020359445205"
    ],
    [
      "5263206579862",
      "21694214378887910101"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Dujella - Lecacheux (2009). Source: https://dujella.github.io/tors/z5old678.html (curve entry 18). Published independent points; exact point coordinates checked.",
  "created_at": "2026-09-26 20:28:36",
  "updated_at": "2026-09-26 20:28:36"
}