{
  "id": 4061,
  "curve_key": "30657788746986376366958004387657588336100686579535921:1728589501740782954412453580670642009435260003280513221102376158971994536307031",
  "ainvs": [
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    "0",
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    "-2000682293681461752792191697520052233697713603839721993736989193429426395383"
  ],
  "rank_lower_bound": 20,
  "torsion": [
    2
  ],
  "naive_height": 362.56417947535175,
  "faltings_height": 28.27529994704089,
  "conductor": "2068433157780159063084093615556099330453046637971536818742205532992224375804129639558855110",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "19",
    "23",
    "31",
    "53",
    "71",
    "79",
    "89",
    "103",
    "107",
    "113",
    "127",
    "151",
    "271",
    "283",
    "293",
    "739",
    "743",
    "977",
    "1471",
    "3191",
    "3617",
    "744701",
    "1489951",
    "14742361",
    "28928843",
    "1705548529"
  ],
  "discriminant": "14946316151938412093963886923582110367207761154009221689493780190885752775897916361128842174340193262341561106853097569140330157857920390191514410000000000",
  "regulator": "7937150229384211320267.90339697123368144714642051803445594914616186298132370768",
  "points": [
    [
      "-23530128896536187096562326",
      "498482997877693975054565702639289163"
    ],
    [
      "26724161812456242995140774",
      "4046528211539539320737169270911091463"
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      "26757874138753429018027174",
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      "-8653314911481750925525526",
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      "27585363237176219939111674",
      "37034880436325929736962597413234081163"
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      "29337421987856213916950674",
      "67168819226629226591167043798086818163"
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      "-20451159919006360924468166",
      "50078513502332318145719276597884333243"
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      "-22310842767756921207636326",
      "33817005294351990379271133298122297163"
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      "33287491773040592069301274",
      "116717212532811949090114327427143410763"
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    [
      "47281118205819088413716374",
      "271104808190343481298434892304974999863"
    ],
    [
      "53901757114096860902182924",
      "346667257379554282137483579560737197163"
    ],
    [
      "80132503007178679446708274",
      "679239756412775944639239900865592443963"
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    [
      "82523652386913173356701274",
      "712242832237452131491387267226785237963"
    ],
    [
      "281374408518341113950040954",
      "4700546203931712840415696986666928324603"
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  ],
  "submitter": "wgxli",
  "history": [],
  "commentary": "specialization at T = 88516/98303 of the rank-9 fibration of X552 given by:\ny^2 + 238(19T - 6)(5T - 3)xy = x(x + (12T - 29)(51T + 22)(79T + 22)(482T + 29))(x + 256(T - 22)(83T - 7)(21T - 2)(7T + 17)).",
  "created_at": "2026-10-08 21:44:26",
  "updated_at": "2026-10-08 21:44:26"
}