{
  "id": 39,
  "curve_key": "-1505664758992227126399291134025916358055376960575:-260961525531561099457995721578616998276609112811677665548304369308086430625",
  "ainvs": [
    "1",
    "-1",
    "1",
    "31368015812338065133318565292206590792820353345",
    "302038802698566087335643188429543498624522041683874493555186062568159847"
  ],
  "rank_lower_bound": 19,
  "naive_height": 342.70099936054265,
  "faltings_height": 26.616101684877602,
  "conductor": "565363502863493379565569563649307108299188776386222378070363275106421667133549554450",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "19",
    "47",
    "61",
    "71",
    "79",
    "83",
    "101",
    "127",
    "137",
    "229",
    "241",
    "293",
    "311",
    "523",
    "541",
    "827",
    "1009",
    "1753",
    "3331",
    "4091",
    "6637",
    "9007",
    "16069",
    "44263",
    "52609",
    "67157"
  ],
  "discriminant": "-39412228697608401237498486986030933067178933520817917493127770273615403601711081236922902433264711434650985878886431089797471702169158680576000000",
  "regulator": "754818738046468728836.6738481003770253068141192531193418878223715648421956502",
  "points": [
    [
      "-499155234006326082923757",
      "402509376386904307636088023311932246"
    ],
    [
      "14139901902190764472167779",
      "53177370026792370019660919624681843910"
    ],
    [
      "165026138566397083648829",
      "558309596396209485460849837556760960"
    ],
    [
      "463343337635697262499219",
      "645016881525945325912024782026024790"
    ],
    [
      "-428490311544140084738931",
      "458176166275251046654351925125281840"
    ],
    [
      "-3076708833879670305775",
      "549492732729622717403028037016638716"
    ],
    [
      "-37665731401560276357421",
      "548455893205160937812792765224762710"
    ],
    [
      "-589425676522172250643765",
      "280659706984671022310703064556433246"
    ],
    [
      "-481732375371853545253165",
      "418490225997586738600806619185884118"
    ],
    [
      "3690858926941989311074375079",
      "224228684581316592254479552957274125288710"
    ],
    [
      "6130049174458433978294529",
      "15193625860788829982804926312716459660"
    ],
    [
      "99629044314032316202835",
      "553310835513576760020037678256777046"
    ],
    [
      "-336069400109872546513581",
      "503527960099926164391149483607861590"
    ],
    [
      "3296316187302021571885259",
      "6018489996489383086719697427657451870"
    ],
    [
      "239450610550684059490919",
      "568576446830597022058144468592457990"
    ],
    [
      "1116036406771517906484819",
      "1314196172527374653201729069765173590"
    ],
    [
      "1104492511976272577147219",
      "1297713008801587828896903435227547990"
    ],
    [
      "-556915090457934898225581",
      "334424588793955899397684278466715990"
    ],
    [
      "142518206539016399870550419",
      "1701397854372553501423223969798389683990"
    ]
  ],
  "submitter": "David Renshaw",
  "commentary": "Found by Elkies (2009). A curve of rank exactly 19, via Dujella's elliptic-curve rank-records tables.",
  "created_at": "2026-05-27 22:12:17",
  "updated_at": "2026-07-01 22:31:41"
}