{
  "id": 815,
  "curve_key": "225815322698297741522603058624117974377303201:-3379573298583672517365771254556694544918594828154333369015278194801",
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  "rank_lower_bound": 26,
  "torsion": [],
  "naive_height": 306.3848742442976,
  "faltings_height": 23.359441307774958,
  "conductor": "2090052314595515427034152500520120902146273491021421311412900199956586310420257693417770027719997020373470",
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    "5",
    "11",
    "13",
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    "41",
    "43",
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    "3710880413",
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  "discriminant": "54042652364004468697205306256620589849594814325453900021062402371369358566895451129178861873106225446892580291379510421382400000",
  "regulator": "20329616818415461343770279453.7116026872027643499553889734867050022518663014845497727820865",
  "points": [
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    [
      "4324298872138091765138961620/4190209",
      "-106999694921945278740013677808166806562890/8577357823"
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    [
      "1765671721608869237059848600/2209",
      "74193070532324067185708545376338243712250/103823"
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    [
      "9905357890663548290472",
      "-963943546114056473677870346643774"
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    [
      "1828089592186501751900",
      "-37691314834129927535175829441150"
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  ],
  "submitter": "thomas",
  "history": [
    {
      "kind": "primes_recorded",
      "user": "Daniel Błażewicz",
      "at": "2026-09-21 20:05:16"
    }
  ],
  "commentary": "specialization at T=355/767 of rank-17 fibration of #302 family:\r\ny^2 - (Lx+B)y = x(x+D)(x+E),\r\nwhere\r\nL = 446667T^2 + 471466T + 239031,\r\np = 318552T^2 + 368554T - 72570,\r\nq = 733413T^2 - 45082T - 14960,\r\nD = 5(7174492962T^4 - 7114589515T^3 - 22069002960T^2 + 3909144679T - 205134150),\r\nE = 882769396002T^4 + 811447034567T^3 - 1174040743T^2 - 32493137198T - 2386325360",
  "created_at": "2026-09-21 19:30:58",
  "updated_at": "2026-09-21 20:05:16"
}