{
  "id": 4115,
  "curve_key": "59991652660782032833331383372945454023709326017949092069105:-6726364297533357942347697685137323959512429492142713588783039773176904079345884455252425",
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  "rank_lower_bound": 21,
  "torsion": [
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  "naive_height": 406.024667192652,
  "faltings_height": 31.88947417773494,
  "conductor": "2354821899258314703620981481029366760380391230269986226723630380510794423225946002025617184809098350",
  "bad_primes": [
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    "61",
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    "467827",
    "1516909",
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  "discriminant": "98764979522445525354120949581381016413251963321297130105295511726385275781802955903383532930732474241183846612083181058902381033816188232188172227912347481626452216029184000",
  "regulator": "17743173740698309216325823.402371547024670638149098713623550246797259747666987801",
  "points": [
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      "259811849413974313073226858333",
      "131228564653906218522650419995287541325209681"
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    [
      "-1867749282542509191529274100379/49",
      "71395078256775630156868023002815012248723735/343"
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    [
      "-1549361648493111001353483420315/121",
      "6198700774470214283649578672853654647295214531/1331"
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      "374204344222382462546269825370339/676",
      "7224133242321136935441139273893288459890532521505/17576"
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  "submitter": "wgxli",
  "history": [],
  "commentary": "specialization at T = 92968/9807 of the rank-9 fibration of X1152 given by:\ny^2 + (6573T^2 + 312188T - 7905)xy = x(x + (16T + 3)(2410T + 9817)(7953T + 478)(8 - 55T))(x - 529(349T - 78)(6T + 13)(25T + 22)(292T + 967)).",
  "created_at": "2026-10-09 15:30:08",
  "updated_at": "2026-10-09 15:30:08"
}