{
  "id": 1958,
  "curve_key": "334839910668435321853222096:-7761084395353258669231315200081661809856",
  "ainvs": [
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    "1",
    "0",
    "-6975831472259069205275460",
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  ],
  "rank_lower_bound": 19,
  "torsion": [],
  "naive_height": 183.69988138573837,
  "faltings_height": 13.316941793451331,
  "conductor": "83381005700353763816706043731041708749035035649707435573880",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "23",
    "431",
    "415553",
    "61915409327",
    "389186320132092517280729790246779969"
  ],
  "discriminant": "-13132481663695722220075359768828762423367212917596484383354832432708508000000",
  "regulator": "87135257878425915.47915851885076405277272554564022128456655773571533425716571",
  "points": [
    [
      "-47281787933694189711634292290998/22785799631862706609",
      "-414501300043231244756596543883196483918257091834/108766814938703411322146655977"
    ],
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      "-1670645055834",
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      "548646589646742/529",
      "-20588618401002392001894/12167"
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      "-85733719901646/289",
      "-16313864026793309194050/4913"
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      "-72384570103506/25",
      "-276917901222134598678/125"
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      "-4900371233848292796/2640625",
      "16914032492027320024800466608/4291015625"
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      "-176598592041746586/237169",
      "428510923042367900666164170/115501303"
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      "111673011618429/100",
      "1607878770943430069133/1000"
    ],
    [
      "424682134599024/169",
      "5944677242224617914640/2197"
    ],
    [
      "-181665463841155851/62500",
      "-33881110912039644271762857/15625000"
    ],
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      "5104385233448799/4225",
      "-418148759544204635012682/274625"
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    [
      "24623983458246/25",
      "-218924198299057100094/125"
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    [
      "173286347297427842958/161823841",
      "-3407954880156107346816217478718/2058561081361"
    ],
    [
      "470350503308316704109/71605444",
      "9514734944746543725761195662875/605925267128"
    ],
    [
      "96347465955577039847366274834/146070727157152009",
      "120623698864008574447075382806187016283202790/55827063791858422095184027"
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      "9142854392256664789386336/39979178222281",
      "687620457260182755097366764057991869960/252784705794264535429"
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  ],
  "submitter": "Ritik Jain",
  "history": [
    {
      "kind": "primes_recorded",
      "user": "Daniel Błażewicz",
      "at": "2026-09-25 20:07:57"
    }
  ],
  "commentary": "Specialization at T = 5 of the rank-17 fibration of X1092 given by:\r\ny^2 + (Lx+B)y = x(x+D)(x+E),\r\nwhere\r\nB = pE + qD + pq(L-p-q),\r\nL = 132987T^2 + 93270T + 585575,\r\np = -48077T^2 + 65376T + 319973,\r\nq = 13974T^2 - 848745T + 719796,\r\nD = 3762979682T^4 + 7417401493T^3 - 91707153902T^2 - 10715099623T + 249952800570,\r\nE = 2431655842T^4 - 17839413059T^3 + 73246802384T^2 + 439113416444T + 183933292704.",
  "created_at": "2026-09-25 20:06:42",
  "updated_at": "2026-09-25 20:07:57"
}