{
  "id": 718,
  "curve_key": "20010775845389933009726276583601:-89777360983172473110048777891454709884509794665",
  "ainvs": [
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    "0",
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  "rank_lower_bound": 19,
  "torsion": [],
  "naive_height": 216.22732404678396,
  "faltings_height": 15.833065686332727,
  "conductor": "126255005317631596807342763298768589860892860901051460856426",
  "bad_primes": [
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    "3",
    "7",
    "17",
    "23",
    "29",
    "281",
    "283",
    "174649",
    "19088231792553041564635095085484211371021801"
  ],
  "discriminant": "-27220232785317536534993615747937996682722280519405708587443003358825187573882312199774208",
  "regulator": "46767289689605553.53181405014226901183782307889438462740462933227404195828984",
  "points": [
    [
      "9170296616792636995237010072169/104487697231642624",
      "-278510771102450767525188587460323376961934781003/33775185040654347567890432"
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      "1973538867265279250378817724214109/1382469544"
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      "109941127711328719866/279841",
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      "2758178830224244794/7225",
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      "827995192677409338/2209",
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      "316100852193049317584477226/1240704149161",
      "5213750144329470126611386766730054225999/1381981889921813909"
    ],
    [
      "79503780342918059059686/198443569",
      "3053582393161354517345274680132973/2795474556503"
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      "2176765857213919365/5776",
      "249242247688980060582686529/438976"
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  "submitter": "wgxli",
  "history": [],
  "commentary": "Specialization at T = 843/1421 of the rank-11 fibration of X163 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 = 36T^2 + 8T - 19,\r\np = 2T + 2,\r\nq = 84T^2 - 113T,\r\nD = 493(T^3 - T),\r\nE = -T(T - 1)(1021T - 1954).",
  "created_at": "2026-09-12 00:30:03",
  "updated_at": "2026-09-12 00:30:03"
}