{
  "id": 1393,
  "curve_key": "553578789308608900457659764387406234524501594481:-412240289790947603409677257969900525797474252885241130627565517081866121",
  "ainvs": [
    "1",
    "0",
    "0",
    "-11532891443929352092867911758070963219260449885",
    "477129965035818985427866235650134910745513387031938136016451076770225"
  ],
  "rank_lower_bound": 28,
  "torsion": [],
  "naive_height": 329.7999556471509,
  "faltings_height": 25.251992674815085,
  "conductor": "4997539447084604265015693653254416670885537251925261031237083539217290415193756279081256913681258637880707649270",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "23",
    "37",
    "101",
    "380869",
    "27746524433989861",
    "7160854931634141712827468527700751",
    "16555589013770658824199467146066474032839750983"
  ],
  "discriminant": "-172526987195500245437889701098090108871004464092403575685298243446871769421269159568154220077452472431447939224976859387240205332480000000",
  "regulator": "5021017574554074272957688056276.070612276864145570149832558688836761170832047605286306248081930",
  "points": [
    [
      "9979786642567883558277080/169",
      "3116475935977456868395509029770118405/2197"
    ],
    [
      "582508810959439436416053575/7396",
      "4817191424263864681080482873823234929335/636056"
    ],
    [
      "168408237839786140518710834/25",
      "2185194713762723409699713228648175190963/125"
    ],
    [
      "299132560911255842434370",
      "-154252178628365940192095606050295185"
    ],
    [
      "8265340719925969487157650/121",
      "-3780287283669568725206379494149968035/1331"
    ],
    [
      "62812359289719005714870",
      "-735699649529220287672796992444185"
    ],
    [
      "-49413902549820718668542830/841",
      "752476838000281127281235704064777825035/24389"
    ],
    [
      "70488428737934341052066",
      "3797984395572601399621306169456687"
    ],
    [
      "63827392553176919046710",
      "1021905299565977464790242645909475"
    ],
    [
      "546526078512949807343048330/12769",
      "-11353946833290380749654589357211254009945/1442897"
    ],
    [
      "106987519251235939919270",
      "21630277237609172934407113791440915"
    ],
    [
      "153205259722909180762370",
      "-48023342840869934879750655232019185"
    ],
    [
      "768809376614381610036557654/12769",
      "-1450913139615677490729753182735706389801/1442897"
    ],
    [
      "441160050354156421526570",
      "-285041776145234400524920411301769385"
    ],
    [
      "247563866682346925674446026/361",
      "3850068255497138092072476947102612629013/6859"
    ],
    [
      "-11116347102077067365653401100904158/247716239521",
      "3707563435298263889893302736104032219751288757972417/123291097288236431"
    ],
    [
      "1708268535666554864384949391350954920434821090395178770/29225646417428739622603764858721",
      "-260568495998290545048253704640524286614877402168407956309656968441567527181232015/157996035136488290927885019145876658461943665519"
    ],
    [
      "-115728805870556383791710",
      "16181585538631593904061205796821295"
    ],
    [
      "-1028316460311646277162583471842990586660333130426/17452974274699059962119489",
      "2249810849314130831229618062481034284074357316483377473591366309116732499/72912866562598474026932322579554016737"
    ],
    [
      "5931905638466656868745042554191856480/94871671363681",
      "633342198595038322194540977113651160906637974067810935/924069907261567949329"
    ],
    [
      "8392645180003754718436109837841290931730815602879570/134146628548899965312354959801",
      "33946837109537453211359858312959979150939636627396629763303615880603631709635/49132588297351593686881183822837554183701549"
    ],
    [
      "177768284713382319354116397775634115735890/2675414513678574721",
      "8944574185156360608124446339250069221140977151303934565593905/4376093756681092140217651519"
    ],
    [
      "-1987176157124083401063591186177571711870/17943611693490289",
      "47837218615437240537468417500658829214974637228851491904345/2403614379928273589468663"
    ],
    [
      "-16922538203612543970324430/361",
      "207448921641428140075251341036342110085/6859"
    ],
    [
      "-17538601447147195999192631668965480546490268006530/189636023521352390840016721",
      "71644749667541744884252420589219713773200984297045732519514962070133125985/2611447263894709351831072352507852708519"
    ],
    [
      "307744484698286157201178785049469360/34123718085601",
      "3854212330153243679397865647633399398121029523323297065/199335439506660607151"
    ],
    [
      "13429172126449206276472636219520543715660309970/222436366598680969059081",
      "99973960323999665112626639184518934329139831733435895231338812638635/104908019590342573925613479810672229"
    ],
    [
      "46733138254919517787476338974580090/1778283591529",
      "32875633510554447638488812444089971506636475119318325/2371382069826526667"
    ]
  ],
  "submitter": "Ritik Jain",
  "history": [
    {
      "kind": "primes_recorded",
      "user": "wgxli",
      "at": "2026-09-24 22:29:50"
    }
  ],
  "commentary": "Specialization at T = 5036/209 of the rank-17 fibration of X1092 given by:\ny^2 - (Lx+B)y = x(x+D)(x+E),\nwhere\nB = pq(L+p+q) - pE - qD,\nL = 1299T^2 - 3766960T + 321877,\np = 1830T^2 - 1401T - 19560,\nq = 24906T^2 + 1589093T - 8337493,\nD = 7(11896740T^4 - 356491276T^3 - 2949777123T^2 + 37369005238T - 96823708920),\nE = 10(57046374T^4 - 254317076T^3 - 379408012933T^2 - 35060842895T + 1673269025580).",
  "created_at": "2026-09-24 21:25:39",
  "updated_at": "2026-09-24 22:29:50"
}