{
  "id": 327,
  "curve_key": "12587786509560732195160650395345772961:-38325993462875858633513211029823600417043549679185709041",
  "ainvs": [
    "1",
    "0",
    "0",
    "-262245552282515254065846883236370270",
    "44358788730180391915082790816530673754979831118248900"
  ],
  "rank_lower_bound": 20,
  "torsion": [],
  "naive_height": 256.27737110101833,
  "faltings_height": 19.347859513271427,
  "conductor": "20104103494321955336468350880904230636927014428004269314605639576859835351810",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "19",
    "37",
    "41",
    "47",
    "53",
    "67",
    "181",
    "497515775378019961778973281628748896957770970223246090192831"
  ],
  "discriminant": "304214595275859552600848995003180962782409909159288730912914252576839066152627207520825504275130200320000000",
  "regulator": "35127044543168812914.5419850411931715282153585140589294332311437217394962193394",
  "points": [
    [
      "13300346987625972273564260/106151809",
      "-126921815258878457468294861989774951090/1093682088127"
    ],
    [
      "-33688166634582792040/529",
      "-3000122613725233862935284941990/12167"
    ],
    [
      "-2100623373568360",
      "-211918990647899567038818670"
    ],
    [
      "-12122782898776960",
      "-218027872156845422981493070"
    ],
    [
      "-6685372494009737455/64",
      "-136054172245105804800590924645/512"
    ],
    [
      "-129747757360393960",
      "-276044063302146916637961070"
    ],
    [
      "30115526577658613405/16",
      "159602682789982699897778101235/64"
    ],
    [
      "1890335766860344187650160/619369",
      "2564222251576741738531089760348085990/487443403"
    ],
    [
      "176958571250987687380/49",
      "-2331337958147719608024398483210/343"
    ],
    [
      "167120388140571616136900/104329",
      "-65122064428459284963995738972655890/33698267"
    ],
    [
      "24789987240215142247704860/173896969",
      "227836860152742171266578411399684967590/2293179330203"
    ],
    [
      "154070655135638090",
      "87245274648428173106770880"
    ],
    [
      "3122757635543465935700/18769",
      "187769141159479781998025697024490/2571353"
    ],
    [
      "905614790834583884540/5041",
      "-19748287388268200023640363787170/357911"
    ],
    [
      "26886519463147669646060/157609",
      "-4237594015421216481362153199426310/62570773"
    ],
    [
      "272527088373601593437120/7921",
      "142254704961815703015440521806003070/704969"
    ],
    [
      "57613267467222487340/289",
      "-6660857143461319173200479070/4913"
    ],
    [
      "129682215442330089596960/1682209",
      "-342208045127931493996874749664883310/2181825073"
    ],
    [
      "140944368806311259946001913660/1011700023889",
      "-104412502605487029724292177925693901668383390/1017601270128344537"
    ],
    [
      "-33926193151924324",
      "-230687523263038492005199918"
    ]
  ],
  "submitter": "7fff-zip",
  "commentary": "New in this search: Mestre quartic family with roots [0,158,863,928,3783,3850], T=47779/20. 20 independent rational points certified exactly by Cremona-Brumer quadratic characters; quartic point box [100000000,50000] plus an integral-x search on the minimal model through 10^12.",
  "created_at": "2026-08-24 19:15:18",
  "updated_at": "2026-08-24 19:15:18"
}