{
  "id": 4549,
  "curve_key": "223785976330416708118719289540228461982612600556331719974800:-105786401638118055921173952594365098300123856340937926283093598461967182635255055393080000",
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  "rank_lower_bound": 15,
  "torsion": [
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    2
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  "family": null,
  "families": [],
  "naive_height": 409.97412129887834,
  "faltings_height": 31.926830732647634,
  "conductor": "643282095696179055572916818493972668921615787215139585868671202490355824559600",
  "bad_primes": [
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    "751",
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  "discriminant": "9534401296453017120398739624809385523393692790911683892529118401746568318018284899910088812214575279969736133856482372451347589624589701142854590205861091414614050064000000",
  "regulator": "19729028045092635.833988058855598983360677549493993813752660893144004",
  "points": [
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      "8794400356769431270419195866721156360293900"
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      "24805282135239169494387608475",
      "4696096704559711195510804435881834068427150"
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      "43354067837485962729656090190",
      "1341462084421087044317999463265179809883900"
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      "-5004331715425800765749781015",
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      "-76220017023904991833362982359",
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    [
      "1808074795756116341293976451435/49",
      "275726256771277602349303688295681660426431550/343"
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  ],
  "submitter": "wgxli",
  "history": [],
  "commentary": "specialization at T = 4206111/3370112 of the rank-5 fibration of X400 given by:\ny^2 = x(x + (286 - 275T)(64T + 19)(T + 7)T)(x + (23 - 36T)(75T - 4)(89T - 81)).",
  "created_at": "2026-10-17 15:01:05",
  "updated_at": "2026-10-17 15:01:05"
}