{
  "id": 404,
  "curve_key": "925823814380557993135966999636853193861857067298387921:-849616014583526099140785474900409816482009802671534404003803710079423992078034969",
  "ainvs": [
    "1",
    "0",
    "0",
    "-19287996132928291523665979159101108205455355568716415",
    "983351868730932985116649853601474646887931496490259148783013795470646286030617"
  ],
  "rank_lower_bound": 27,
  "torsion": [],
  "naive_height": 372.787571081976,
  "faltings_height": 29.001326825301682,
  "conductor": "161556735231476753254583770823345475052543520784292394332312680868697134445526610416074943640483611548766974670305841924180347140444710",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "19",
    "29",
    "2503",
    "117466975445805874169003",
    "40102956406526573322891878089",
    "1301247044069409176793485972536865652985877115046209823816786383362471611"
  ],
  "discriminant": "41505940491909352111741176345891872662987590833015371871277614219536506459943277907639290641022780946037539336622788189039872262087323170328449646922854400000",
  "regulator": "1976469480783608859731990660622237.7497697010948215230220644149035445572892995171740078191824",
  "points": [
    [
      "4759109245492436204950374",
      "944280666776535660774757868974298693613"
    ],
    [
      "55224962092529877761984574",
      "294275221747047230540208884270266031613"
    ],
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      "94083069928218594952126374",
      "38287647939482588317402153098629189613"
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      "64512185924282150488730454",
      "86771650364837312936060853603981639693"
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      "-96018067638139622573585466",
      "1396464234395918627024207379268258146093"
    ],
    [
      "-82935642627004905134963226",
      "1418645926850988554239990474034411583213"
    ],
    [
      "-65882272521685879566150426",
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    ],
    [
      "96849759689848451223648414",
      "154119467388364918206606534946249028133"
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      "194026267372675997908490454",
      "2131976588065035976704540194051184999693"
    ],
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      "104093572471203561663091014",
      "321711699539274739973847345583256491053"
    ],
    [
      "243856890385518290371388874",
      "3283455432415195363131621627105571514613"
    ],
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      "105202974301014643984073574",
      "344308971938354143263978538057439813613"
    ],
    [
      "64795699284404949366604074",
      "74941913960594764916126825367973073313"
    ],
    [
      "65420750562084501891014502",
      "38849630479946419673959986447731415213"
    ],
    [
      "544567444081111599349471974",
      "12327742217570537365313509413378740991213"
    ],
    [
      "64911478819199283996282534",
      "69599120994074300878944398463782747373"
    ],
    [
      "53586476468025799846101894",
      "321947581983001725284326399721384354733"
    ],
    [
      "65604542362910079658749414",
      "18187129015601816244242865292521401133"
    ],
    [
      "104583217355769396827671974",
      "331731422080656625573614711028904136813"
    ],
    [
      "450219412340337856280753574",
      "9140999922505833561679568114076731592813"
    ],
    [
      "51349876615569498923502054",
      "358211538748101910774992776442920740653"
    ],
    [
      "105917631778970072538118254",
      "358684660244163904785731053608290165493"
    ],
    [
      "95670676707436100993651814",
      "117125125218363469753775204927896356333"
    ],
    [
      "124402096049605714281623814",
      "713524223978548046643207349812974112333"
    ],
    [
      "98892241676814576116196774",
      "207491501477298577199402401048710140013"
    ]
  ],
  "submitter": "NDElkies",
  "commentary": "Noam D. Elkies and Zev Klagsbrun, January 2026.  The cubic field generated by the x-coordinate of a 2-torsion point has a class group of 2-rank at least 25, the highest known for a real cubic number field.",
  "created_at": "2026-08-28 17:06:58",
  "updated_at": "2026-08-28 17:25:54"
}