{
  "id": 578,
  "curve_key": "51171453423952276841322841:-322175782507735566680361621790741158365",
  "ainvs": [
    "1",
    "1",
    "0",
    "-1066071946332339100860892",
    "372888637161286783309817106150962080"
  ],
  "rank_lower_bound": 21,
  "torsion": [],
  "naive_height": 177.59167217430047,
  "faltings_height": 12.782241883457992,
  "conductor": "110950909706648386027354584054003218623680117123767799415377945462",
  "bad_primes": [
    "2",
    "3",
    "13",
    "29",
    "103",
    "14863288607",
    "14043772972837",
    "45014284458994007",
    "50681794094157328259"
  ],
  "discriminant": "17474605846665310266071202941394451872517553379301959211863682296952843632",
  "regulator": "37117101300010566666.846194974001281678469799609939146074267010474601308284544946",
  "points": [
    [
      "61858971848437/169",
      "391254774284499868465/2197"
    ],
    [
      "73574306667424843/323761",
      "69507492283158722616094808/184220009"
    ],
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      "-416943626680647083695069976/394218443854225",
      "4409120454478378562063858518599877386512/7827181578526786850375"
    ],
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      "4314807029600292799/1014049",
      "-8717223840680811112728601588/1021147343"
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      "442240803098693385028/1059567601",
      "-874201507847005934797419017120/34489984980151"
    ],
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      "4023179527744616264/4687225",
      "3047785763409394855542944632/10147842125"
    ],
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      "-114655070868852/121",
      "971052417988300612100/1331"
    ],
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      "-125913479099603/289",
      "-4267975874652115647715/4913"
    ],
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      "2201613806751601430797/8529630736",
      "-267047159103931299088873191669143/787762576254016"
    ],
    [
      "621765897644415875044/510262921",
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    ],
    [
      "715283474918641960/908209",
      "-127764856714507684733275120/865523177"
    ],
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      "78448879153189416/323761",
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      "-782571968688109681570001/1786911256516",
      "2076589533177278693621972648413226351/2388660769792789064"
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      "3987553327522614003625087/18490404202209",
      "-31101796404084696532661942241276038644/79509607118496203823"
    ],
    [
      "517055477051800264/1456849",
      "348288045006906969532928392/1758416743"
    ],
    [
      "-137449703296960336613/274001809",
      "4009383620762187785684480897669/4535551944377"
    ],
    [
      "1130887581308278652979854407/550669253793649",
      "33807995626001559903812749887666461376004/12922193589075818655607"
    ],
    [
      "8729299821502529631624839119/9342095656503289",
      "396258677302115013294241233685316926338652/902955743447123307206413"
    ],
    [
      "3665121207599248393254841/3004009971264",
      "4907418868939931541104633230501330889/5206574114274534912"
    ],
    [
      "322996487033265730147/168636196",
      "5068834466174763452209085296061/2189909641256"
    ],
    [
      "2733550206698179/1225",
      "129376547831411504601272/42875"
    ]
  ],
  "submitter": "wgxli",
  "history": [],
  "commentary": "Specialization at T = 7/26 of the rank-16 fibration of X948 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 = 2056204T^2 - 19826992T + 730903,\r\np = -1352(15493T - 925),\r\nq = 4336938T^2 - 705587T + 21815,\r\nD = -2028(142509543284T^3 + 23186595908T^2 - 2342619577T - 2236095),\r\nE = 12(8320656394176T^4 - 4943881953560T^3 + 753235556749T^2 - 40844263700T + 858131775).",
  "created_at": "2026-09-04 18:34:23",
  "updated_at": "2026-09-04 18:34:23"
}