{
  "id": 691,
  "curve_key": "8193618433293337267538021497111728717921:-357413022739447159010259151362690112177379059598301154891281",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-170700384026944526407042114523161014957",
    "413672480022508285934178743417257094770023329091786960789"
  ],
  "rank_lower_bound": 25,
  "torsion": [],
  "naive_height": 275.71252271462964,
  "faltings_height": 21.02839461337832,
  "conductor": "272477462251985379286820733512680714450495871001031119894781628331624714896491284195957326271170",
  "bad_primes": [
    "2",
    "5",
    "7",
    "13",
    "19",
    "43",
    "53",
    "59",
    "6650521999543582597820284157728903",
    "1355626871643268662547104228934136167711647486605987"
  ],
  "discriminant": "244408358275683636638671816734289148186540606903620569817329948906217619582004929679836204768521293229032073369600000",
  "regulator": "313336172249796547387045223.5830466859517581310574560774181882343732612873751640512574239",
  "points": [
    [
      "2333539875972734387",
      "5295602380421415127245162776"
    ],
    [
      "2431361028243932249",
      "-3607110965222310192437772838"
    ],
    [
      "2233187909552714527",
      "-6603305290521731591676766824"
    ],
    [
      "22599181096082416903/9",
      "-25226156227929874876948117048/27"
    ],
    [
      "2425534977638519887",
      "-3728630257046553197288042664"
    ],
    [
      "2514010933252338647",
      "-647323965120163402770729224"
    ],
    [
      "-127134412399897897307/9",
      "67282047572880641718572398642/27"
    ],
    [
      "2316872610659823317",
      "-5533369056476508640945357844"
    ],
    [
      "-11375247088445700433",
      "29724018108526195069914290776"
    ],
    [
      "1573534378649378047",
      "-12205148293943229864184313624"
    ],
    [
      "-14135877523050558993",
      "-1413603930352666456929092424"
    ],
    [
      "1060084045522050367",
      "15294019277415375572913764776"
    ],
    [
      "13960132232968075933/9",
      "333563888597802914327741604452/27"
    ],
    [
      "11626552370549162767",
      "-809160133062991418728533224"
    ],
    [
      "107660914395643514983/9",
      "246683308349613695272716174952/27"
    ],
    [
      "8610650185976897163/4",
      "59966657533967103126120546433/8"
    ],
    [
      "167540544089577355207/81",
      "6075011888020530672288687726904/729"
    ],
    [
      "11873036895121820727",
      "-7789141244448996733914866824"
    ],
    [
      "15378337469903858863",
      "-37755232508475130119833034152"
    ],
    [
      "11717193449300755647",
      "4714580939652690145154625576"
    ],
    [
      "-2526933945886573649167/529",
      "407200102799048210308118121972532/12167"
    ],
    [
      "-320365069336459081193/121",
      "38737964951732650192855654292936/1331"
    ],
    [
      "-12012410170854264941",
      "27033844888151270638438555288"
    ],
    [
      "-673732993617873256193/81",
      "25856947855489241736417136074904/729"
    ],
    [
      "82939415766968813647",
      "746184763762427143501762015576"
    ]
  ],
  "submitter": "FNacc",
  "history": [],
  "commentary": null,
  "created_at": "2026-09-10 02:08:55",
  "updated_at": "2026-09-10 02:08:55"
}