{
  "id": 1854,
  "curve_key": "445750796351367656221419398038096:-16724115395981966268308315747711953361954648926144",
  "ainvs": [
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    "1",
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  "rank_lower_bound": 23,
  "torsion": [],
  "naive_height": 226.6818723544151,
  "faltings_height": 16.930597894483267,
  "conductor": "35819382478169004066817345528936202249131130668789846039066817241325534575720",
  "bad_primes": [
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    "17",
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    "29",
    "43",
    "73",
    "5581215658969",
    "259847275952693991576527559572005224841853567845686889"
  ],
  "discriminant": "-110606555832998722030477096825275978976522348905896291580088795583477627581705030471079666400000",
  "regulator": "10239883025727041299873.1379026433922077680198646200983468187820664034092684393908861",
  "points": [
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      "206078296304415223973232652829690/156464230318026409",
      "6003761463219877749208125183438845197368668455590/61890302032592436073761173"
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      "-575843790419701166/225",
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      "-3581102869925986",
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      "25782532173634620182/12769",
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      "1041574262328412490/361",
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      "92046473970609936839460"
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      "1307255052854990",
      "97215289710475218784110"
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      "5378038519486888999/9025",
      "101570424722138390603254581282/857375"
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    [
      "-5108613930423414235481134810/3174159134689",
      "981678637831881810918353612350912398597690/5655135875067212113"
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      "10565515805969849802377319898723814479015650900/61041668193467173357237"
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      "-3301251320552626326178877275/2312023645156",
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      "200771279792409144662174/2082005641",
      "12908097691206435091080199750831262010/94999835393189"
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      "506704805807752654390/12321",
      "11376212640297915984804773980010/1367631"
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  ],
  "submitter": "Ritik Jain",
  "history": [
    {
      "kind": "primes_recorded",
      "user": "Daniel Błażewicz",
      "at": "2026-09-25 17:18:09"
    }
  ],
  "commentary": "Specialization at T = 32/49 of the rank-17 fibration of X1092 given by:\r\ny^2 - (Lx+B)y = x(x+D)(x+E),\r\nwhere\r\nB = pq(L+p+q) - pE - qD,\r\nL = 337637T^2 - 5806T - 128944,\r\np = 400307T^2 - 728353T - 164164,\r\nq = 30116T^2 + 59665T - 51226,\r\nD = 20(17239450100T^4 - 50269926206T^3 + 33049656247T^2 - 4679416867T - 19532604),\r\nE = 82122368860T^4 + 49706770391T^3 - 201865310888T^2 + 62291384169T + 16126031988.",
  "created_at": "2026-09-25 17:14:15",
  "updated_at": "2026-09-25 17:18:09"
}