{
  "id": 332,
  "curve_key": "4219018142004858523653697611937:-8667679642855220694082068847755741501442841201",
  "ainvs": [
    "1",
    "1",
    "1",
    "-87896211291767885909452033582",
    "10032036623674987328062504411246312614248555"
  ],
  "rank_lower_bound": 19,
  "torsion": [],
  "naive_height": 211.55186061824637,
  "faltings_height": 15.346717192653273,
  "conductor": "11000203474134513163114551624790609684216808458508386590177281881926",
  "bad_primes": [
    "2",
    "3",
    "7",
    "17",
    "19",
    "37",
    "61",
    "71",
    "73",
    "69316422129706338470662069609749205202946553954322684531"
  ],
  "discriminant": "-17167909180637480883395526936559530872769554325924464584539224547488746121889587183616",
  "regulator": "1849713008892069162.162532891599780163265102933993712449046864025910208639975",
  "points": [
    [
      "22379054239159361",
      "-3347531525037033343948377"
    ],
    [
      "3646730481788423",
      "-219513249242184999428259"
    ],
    [
      "137922453018922928609/46225",
      "-1612058146940998846331031767007/9938375"
    ],
    [
      "13210141533447499/9",
      "-1489475020709247134433845/27"
    ],
    [
      "-20645141097552823/1849",
      "263839353057070445828104437/79507"
    ],
    [
      "58101106471791461/2401",
      "331077574868547035277880935/117649"
    ],
    [
      "1416391468490569/9",
      "8410613058716250897821/27"
    ],
    [
      "4242297178834205072017/25411681",
      "13481525034579180739750184946759/128100283921"
    ],
    [
      "2686808745548745585959/15856324",
      "3734203274231222545781528180805/63139882168"
    ],
    [
      "1888414406611431087089/10975969",
      "1774095388506234845272904301831/36363385297"
    ],
    [
      "173995554471825",
      "78146159707741567255"
    ],
    [
      "6273773583732509/25",
      "242975691725347075655067/125"
    ],
    [
      "109656060388391608012625/424813321",
      "18661640351301329963039721473528805/8755827359131"
    ],
    [
      "3037767624896724125/24649",
      "4005752138987940151799504415/3869893"
    ],
    [
      "591163905736875089833/4076361",
      "4764648893991205856798967456845/8230172859"
    ],
    [
      "33321364225744085475105/25694761",
      "5935795661282938457835449233218755/130246743509"
    ],
    [
      "152431711876145",
      "419144946573253064439"
    ],
    [
      "-75536487613842984167/692224",
      "2465361180213569582344333063779/575930368"
    ],
    [
      "-7068944142404731327/196249",
      "315279922533780173756729954853/86938307"
    ]
  ],
  "submitter": "7fff-zip",
  "commentary": "New in this search: Mestre quartic family with roots [0,115,206,234,731,784], T=15123/14. 19 independent rational points certified exactly by Cremona-Brumer quadratic characters; quartic point box [10000000,10000].",
  "created_at": "2026-08-24 19:17:54",
  "updated_at": "2026-08-24 19:17:54"
}