{
  "id": 4076,
  "curve_key": "471211810821338985001180838299315920393701047302053465425:-10211442725371495007431123845902855484448305409241563457657294978395065721833428865625",
  "ainvs": [
    "1",
    "0",
    "0",
    "-9816912725444562187524600797902415008202105152126113863",
    "11818799450661452554897134080088006676176269596921055787278149418755224711667070217"
  ],
  "rank_lower_bound": 21,
  "torsion": [
    2
  ],
  "naive_height": 391.48470815733606,
  "faltings_height": 30.416819731225903,
  "conductor": "36002324741262229107384053035934129095312333739830493609470477957959545215672356665910453744176850",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "37",
    "43",
    "53",
    "59",
    "73",
    "211",
    "241",
    "283",
    "331",
    "337",
    "347",
    "397",
    "457",
    "619",
    "967",
    "2861",
    "4603",
    "5413",
    "5641",
    "6607",
    "7487",
    "19087",
    "70051",
    "10951669",
    "25632109",
    "12957651503"
  ],
  "discriminant": "205194931593499080300675582154453277266288091437637331516748908813508343496007999587380988696481051980236176662342201627615903877404833910853213181972238372864000000",
  "regulator": "672735844734286815385534.77350783131017871343439993342362289574721168368987165780",
  "points": [
    [
      "1869897417259948620991895302",
      "553709463041026883056968832624507047349"
    ],
    [
      "1696965298890279827328971152",
      "6824609496062322097493151544133690686099"
    ],
    [
      "1744897658693291519236235062",
      "1387517478609645368162848745620016490469"
    ],
    [
      "1926129114353817515108389342",
      "7486370898292665355827763540834505169229"
    ],
    [
      "1926743210681463891444921658",
      "7540175168721055487804954314534546262617"
    ],
    [
      "1930713891470445761027216242",
      "7885883241135290689233565324083376685329"
    ],
    [
      "1955292075047400227986452342",
      "9963740608937193660252887178031686032229"
    ],
    [
      "261868637349197478945870262",
      "96260145346144799762049937107658472548069"
    ],
    [
      "598894616579718327071458902",
      "78449420978651560301550760277687905721349"
    ],
    [
      "602711195776124031007943542",
      "78236676728338304792757998084462237328229"
    ],
    [
      "623145611592757396897461718",
      "77093497269796930544351760561208991103877"
    ],
    [
      "880726230364795706784130612",
      "62096275921272152565563522678492801946919"
    ],
    [
      "905454435169859836309146262",
      "60600058174883423713432922883066084505669"
    ],
    [
      "1292366056513492196479180402",
      "35920431607153238174805176933027477599249"
    ],
    [
      "2002162483092525072614823538",
      "13773995687681822311532644537985634467197"
    ],
    [
      "7173118156016435811964394902",
      "557210776660029310944556863648683401197349"
    ],
    [
      "8475036388088123478580443862",
      "733041690208686838016547459501982954561669"
    ],
    [
      "13877420898739704655340323342",
      "1596288850107710156307070708892320348698229"
    ],
    [
      "49478928951635917680181143046/25",
      "1489912678370525470283419649452539600925841/125"
    ],
    [
      "453013093513374335546189523142/49",
      "289275828049811647676184911633571859669999075/343"
    ],
    [
      "327689495664949077185270113942/121",
      "95008074523507178837076717621467062009968719/1331"
    ]
  ],
  "submitter": "wgxli",
  "history": [],
  "commentary": "specialization at T = -83339/23895 of the rank-9 fibration of X1008 given by:\ny^2 + (7920T^2 + 62574T - 34198)xy = x(x + (-50T - 56)(512T + 71)(6241T - 764)(T + 61))(x - 2(625T - 67)(T + 8)(32T + 67)(6889T + 17269)).",
  "created_at": "2026-10-09 04:59:18",
  "updated_at": "2026-10-09 04:59:18"
}