{
  "id": 4108,
  "curve_key": "474369471870318376458526556962949607370037506741009:-34427706694818850344486467400631919749524705627246119199058294956141785245177",
  "ainvs": [
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    "39846882748632928639451929038284388824128635346592921012307735996626765201"
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  "rank_lower_bound": 20,
  "torsion": [
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  "naive_height": 352.4654872838507,
  "faltings_height": 27.42685184245572,
  "conductor": "1213249524563722385101574358389528895083959754877740265336233395688563597023994735590",
  "bad_primes": [
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    "3",
    "5",
    "7",
    "13",
    "17",
    "29",
    "59",
    "67",
    "71",
    "73",
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    "10369",
    "55343",
    "381739",
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    "565891",
    "678553",
    "1639459"
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  "discriminant": "-624144291499869793483633050099603743097969360900672930318672052507220688727755817933474305771393064963270595742330237843386118254198599425159639859200",
  "regulator": "18213594436607546135466.6253825752304024232600212584432159860491792143809722189",
  "points": [
    [
      "165935700459318597125738",
      "6181549921111238304016076841685310825"
    ],
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      "3770321235677716831080776",
      "7495483331712435287351730753337667807"
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      "21198100475177675074524476686439130449"
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      "8038706514295944406489766",
      "21905945419784242626511485510699512897"
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      "9995265922069721061619046",
      "30653664442623639399950414380994950337"
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      "19840329713549776039072478",
      "87485382612182931260023674061632362705"
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    [
      "-16971986195852715505702505506/6889",
      "4012348382189439797629950121107281778241819/571787"
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  ],
  "submitter": "wgxli",
  "history": [],
  "commentary": "specialization at T = 39757/56373 of the rank-9 fibration of X720 given by:\ny^2 + (355T - 3074)(T + 34)xy = x(x + (181 - 7T)(32T + 259)(47T + 529)(T - 97))(x + (12T - 371)(83T - 47)(6T + 23)(42T + 47)).",
  "created_at": "2026-10-09 15:23:15",
  "updated_at": "2026-10-09 15:23:15"
}