{
  "id": 4059,
  "curve_key": "15607054787921788414935097165843323208612220610726587761:-42429163444986537288667658693977523027544131969638270098035421218999060610018544009",
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  "rank_lower_bound": 20,
  "torsion": [
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  "naive_height": 381.26195419111133,
  "faltings_height": 29.802060686639056,
  "conductor": "10440871783541742304283973928724932391253078912604073640431645403950958428574441994981529610",
  "bad_primes": [
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    "5",
    "11",
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    "4049",
    "5851",
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    "325634333",
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  "discriminant": "1158179964417361775568351695694005473217098903122994566856378459503457310809857332089075863659209449861520528072033365424182231547165303577500705206329926656000000",
  "regulator": "66662257918157868589023.1508276224478262659618000762461513995118445217507979058",
  "points": [
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      "75638783335376039285665865782312354123"
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      "6199659826088295838745600800477663073143"
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      "17834893719053749033027879954",
      "2380595384506970723972787691683117586751263"
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      "-1716363932695580699444978207054/2809",
      "660032788961308325104147466463113715659041091/148877"
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      "9193782448818600488288801962866/18769",
      "6981168060591019399786974874913545687455059079/2571353"
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  ],
  "submitter": "wgxli",
  "history": [],
  "commentary": "specialization at T = -539905/1824 of the rank-9 fibration of X440 given by:\ny^2 + 15(T^2 + 128T - 16)xy = x(x + (127T - 55)(13T - 55)(52T - 75)(7 - T))(x + (178T - 115)(43T - 55)(4T - 3)(8T + 115)).",
  "created_at": "2026-10-08 21:08:37",
  "updated_at": "2026-10-08 21:08:37"
}