{
  "id": 4118,
  "curve_key": "8338537369200931085433105061374919528707729082517551022041:-566165194648862405674732414365410648232559304051318621090671225758720319819520906706589",
  "ainvs": [
    "1",
    "0",
    "1",
    "-173719528525019397613189688778644156848077689219115646293",
    "655283790102850006567977331426970882151340170628667781827093572298216118282111782608"
  ],
  "rank_lower_bound": 22,
  "torsion": [
    2
  ],
  "naive_height": 400.10471437876686,
  "faltings_height": 31.36292651799785,
  "conductor": "2035380499394781053410535073119755867113480721020446687608912956074864478189031910388141364236880110",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "19",
    "23",
    "29",
    "41",
    "59",
    "61",
    "103",
    "109",
    "163",
    "167",
    "173",
    "191",
    "199",
    "307",
    "353",
    "797",
    "1459",
    "1549",
    "11059",
    "20389",
    "72227",
    "508531",
    "5809451",
    "117291869",
    "61056459470068873"
  ],
  "discriminant": "150026346875966862017364938255318645641599737286555156517681565010052465804753076067620968066820782997435911180330404521388478424637661808904812672601214271499627506250000",
  "regulator": "2331918887459416048117563.440644624864126571131197485594214075931269180369794431634",
  "points": [
    [
      "191117042808107853266177519",
      "788726827375293859582996359378326600734890"
    ],
    [
      "4149949109450523098556090152",
      "76336970407916205764964138831599312936712"
    ],
    [
      "4196649478671770612751480119",
      "12435960133123625871021049286010484781190"
    ],
    [
      "10602022632913948480268079044",
      "72134153544336476464025697668463672817215"
    ],
    [
      "10619284801749662092402530119",
      "89638137807819322987250604007802407068690"
    ],
    [
      "1613366449382728480010992319",
      "615800329225946464263658485253887854287290"
    ],
    [
      "2241830780646673410911794619",
      "526403845693493557536478107899321889054690"
    ],
    [
      "2779564317805939663184591759",
      "440334009035000136135646317685033168692810"
    ],
    [
      "4114054819215760234326732119",
      "101115496382680566329755381325150091054690"
    ],
    [
      "-1715465733414899949788849557",
      "973778915894739579299440131056261770090458"
    ],
    [
      "10672780528256875837410121184",
      "130119481381752918654548073278680600782960"
    ],
    [
      "10878754273380083716898731994",
      "230006223868147999631757656660604591016815"
    ],
    [
      "11079137694383090107941380204",
      "300924182507223035392205252027626197863220"
    ],
    [
      "11094451502510873834604506774",
      "305846431584865575626110795901645784385530"
    ],
    [
      "12075234229654685099761023119",
      "564167681424666903737611356303532116687690"
    ],
    [
      "13482589727422206091761395324",
      "874049691843638270039403921419630339419620"
    ],
    [
      "-13727281106163625058036081881",
      "673227903469164898472176538902563997385190"
    ],
    [
      "14985724870693344218925970394",
      "1190522652383654084680336178440977353436015"
    ],
    [
      "15464406033143522269721946119",
      "1291159936129504100913673029994565395217190"
    ],
    [
      "47537688649719546136735031144",
      "9991208207415038582886686900624682674232015"
    ],
    [
      "207937535137955266739027362771/9",
      "80886100302921380960466895545457705390868230/27"
    ],
    [
      "1252641227049992627355702427511/529",
      "6170522012895601096698950228233833300484332810/12167"
    ]
  ],
  "submitter": "wgxli",
  "history": [],
  "commentary": "specialization at T = -97053/246469 of the rank-9 fibration of X1008 given by:\ny^2 + (288708T^2 + 90128T + 5816)xy = x(x + (506T - 173)(27T - 97)(73T - 12)(5093T + 1977))(x + 4(4779T - 1945)(T - 48)(59T - 17)(199T + 80)).",
  "created_at": "2026-10-09 17:51:08",
  "updated_at": "2026-10-09 17:51:08"
}