{
  "id": 542,
  "curve_key": "2597464729611270737338807353181418832708909376:-127579539098757138169689270104742791100070044924769647828991452309376",
  "ainvs": [
    "0",
    "1",
    "0",
    "-54113848533568140361225153191279559014768945",
    "147661503586524465474159358005052226244960662130382591800920369043"
  ],
  "rank_lower_bound": 26,
  "torsion": [],
  "naive_height": 313.71259515012196,
  "faltings_height": 24.066695366499992,
  "conductor": "13858119093380870911402836699917707730917559748643075892856552587147896304378790356681414169480",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "17",
    "19",
    "31",
    "41",
    "59",
    "71",
    "107",
    "109",
    "127",
    "34634663044790853665781117256440766636432529436532867313481217347957006763"
  ],
  "discriminant": "722277800241862558247745792286000446849914177976842506688452357308161888108929747302648556648102151776258683140249105325544020000000",
  "regulator": "319376359427026699537144218.811704398751567924054406595344856994726103082917876605303291831",
  "points": [
    [
      "463258392246256108402548539/16129",
      "-9670428945943007908612524840155737452090/2048383"
    ],
    [
      "618346097591468452406422299/126025",
      "-735623789789511244635378943525989929118/44738875"
    ],
    [
      "29243161090096769780811670292145369/10834182907024",
      "-5200196743287718422965396541881952356399993412190875/35661059732322520768"
    ],
    [
      "1086564072638274496220516344814621457/3888456654889",
      "1132228128779567049165879938364310240724310525915169866/7667713781538752213"
    ],
    [
      "9577034980207489886273847660947679/2683872892009",
      "2662948257154870023417046927989572010618580837350/4396862816952420277"
    ],
    [
      "1944590826107820969183528801/724201",
      "90822747450981073444426530167193732585690/616295051"
    ],
    [
      "2273335591534512359709313491743406608451/747683678873335681",
      "68532011847466007928314778714678043662215428012882595912070/646512387888978843803609921"
    ],
    [
      "70341205449114774654485352202746331/14078997335601",
      "-2369990593776010637734976231185477886374832535824650/52827199723644736599"
    ],
    [
      "-24903181690476962243687312181/35485849",
      "90993606704516611026770496637554337786127250/211389202493"
    ],
    [
      "536715243879219071964844316369464488561/39684966343517881",
      "-10867192601129420288755330982592210811533808129541917125750/7905676234678286155869779"
    ],
    [
      "-89879781952122042540868190825409/2131071512761",
      "-1204650835117111998142186335413587895103377389197750/3110978684687250259"
    ],
    [
      "161338359469864372784769/49",
      "24690299037581828526680868054609750/343"
    ],
    [
      "61947683284548929115971646/5041",
      "414071172590296198816402280795372072625/357911"
    ],
    [
      "1208012293120536393669555728376488722269039/28242484780909296769",
      "1309209453614681724186055037123711917141414023447341030451881550/150090897683781035590332919103"
    ],
    [
      "8146235081033964942814631901/2515396",
      "318596559655511591726893151862736743142875/3989418056"
    ],
    [
      "325240380464434950102147081262804679/92599299859609",
      "27105738931596700323178626901038461104764500639083050/891069450451938044477"
    ],
    [
      "1901275846139021277246056622798046443/216772883257681",
      "-1882103370194226439720653141194559299033595924675027498/3191592465735438218329"
    ],
    [
      "760950591440087347814120498199/138886225",
      "-204736986965344611166480954583422604222584482/1636774161625"
    ],
    [
      "21769718603641580521091981908803376405609/2520876527982746649",
      "-2279553241511384059227102461525136314378335064194804590898610/4002463331366847495485599107"
    ],
    [
      "27726587581638663512504657091938658496779/5658571247560374649",
      "-165592686322256639098183497430571699226485082569118635565390/13460468707811116072653794893"
    ],
    [
      "208495835569894820274601826984401854/42556665461209",
      "3276105967670823309610460502238777141082068287139875/277620407299473588323"
    ],
    [
      "19375015165575160397384026307244011589980723451/2103290416171621509192721",
      "-2002235552720523505496620536826128796526379903883309199960935626513450/3050344316738427953253214471280635769"
    ],
    [
      "22899598222771050507806736069690542548731144081/4538378219933617255532176",
      "-536541121295189239650939635084114684923197336621762890318249344641375/9668320297373739172628243027644191424"
    ],
    [
      "25265952281542283246499666647405421099/3321512317948969",
      "-80349084239714038184444076812931321698662860981153998910/191427267919469986677547"
    ],
    [
      "150940712012002841731922418161269417471808809/29659343948684348771889",
      "-326029472639582640861959778804984802302098626574531964756957074750/5107899110061461374331207906970537"
    ],
    [
      "2152516194917313372124970158676364129/396516895703824",
      "-930120684248276603035968078887018477591121864449961465/7895734677622198687168"
    ]
  ],
  "submitter": "wgxli",
  "history": [],
  "commentary": "Specialization at T = 1889/8 of the rank-16 fibration of X948 given by:\r\ny^2 + (Lx+B)y = x(x+D)(x+E),\r\nwhere\r\nB = pE + qD + pq(L-p-q),\r\nL = 38104T^2 + 695028T + 78468859,\r\np = 72T^2 + 537067T + 2394620,\r\nq = -3786T^2 + 278773T + 146946125,\r\nD = 900018198T^4 - 74161080925T^3 - 2169781853671T^2 + 80721528900062T + 339935259286920,\r\nE = 65158368T^4 - 55322669902T^3 - 73322018893T^2 + 82814330071091T - 68006574064560.",
  "created_at": "2026-09-02 22:55:57",
  "updated_at": "2026-09-02 22:55:57"
}