{
  "id": 40,
  "curve_key": "11737808320143340870262567384110164924996363543449272977921:-830917597293950141847936654026788953089540835356843717953963823812788614617047247539969",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-244537673336319601463803487168961769270757573821859853707",
    "961710182053183034546222979258806817743270682028964434238957830989898438151121499931"
  ],
  "rank_lower_bound": 20,
  "naive_height": 401.13049623842045,
  "faltings_height": 31.462688360849253,
  "conductor": "14143803817470093613466453371895612334117548667434143819728526037275098905399795800409355189270",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "19",
    "23",
    "31",
    "79",
    "131",
    "137",
    "227",
    "229",
    "337",
    "443",
    "593",
    "751",
    "1093",
    "1297",
    "2113",
    "8231",
    "8629",
    "19937",
    "33073",
    "47419",
    "157559",
    "479081",
    "858259",
    "2391953",
    "11332579"
  ],
  "discriminant": "536322869068731689907926014223523897218983690620200910078755027869276074296716149126908879546977218241763631376739573056546560007049072199214175253755603358448062903360000",
  "regulator": "2345864571013562003762503.94206244554266939212953056905157720878181020686213493",
  "points": [
    [
      "-5976635286513806621064126789",
      "-1486518161621811752215471892311622350764326"
    ],
    [
      "595416388787490259443766591",
      "903504029373113768509734316584679010931354"
    ],
    [
      "2434562872293108275107029075",
      "617088105910990842809058933920186352787402"
    ],
    [
      "3513074027344435171140978981",
      "382084415613590558839076708139976548338374"
    ],
    [
      "399682145249051758133327419",
      "929535737737305075763667416604801178363754"
    ],
    [
      "-10714754038296881855524018251",
      "-1533542840817584957359022971329370697480444"
    ],
    [
      "-16034220456847626275437501599",
      "-871976826237835562350053313866844829289386"
    ],
    [
      "1185828672355214392425799131",
      "820608248516937017244986013572105379548074"
    ],
    [
      "-11190697582885409770718510409",
      "-1515528657208794070421971888182751388116946"
    ],
    [
      "2634316446310680332042122261",
      "579484021184216876019568884495793999507014"
    ],
    [
      "64222149978369055569434725591",
      "15815822465644868585416444171217848754979354"
    ],
    [
      "23945425437351916471937562579",
      "2972551260335618106366053972465493213480034"
    ],
    [
      "251112537077876411029986504415821/72361",
      "7660680492845270503732516891131042427064917041476/19465109"
    ],
    [
      "13094114400583295432756346651",
      "69052082853368511623611930199368498525114"
    ],
    [
      "2689776334541089917424552236511",
      "4411303346731260129651357011579276750542331014"
    ],
    [
      "-2627014038979941829331861469",
      "-1259358775896763343051694775385987771517806"
    ],
    [
      "13434870681765045829611551147217379/1026169",
      "67909287018595777234819162150437056031048512222738/1039509197"
    ],
    [
      "-2128476924703349108908527744522501/243049",
      "-186847352402051756015896357808242938299356659058862/119823157"
    ],
    [
      "-7364938748841807757773625709",
      "-1537278043534293249189664536251504660398646"
    ],
    [
      "785686589410787916270883192839",
      "696287187804791686384919800041247659097028446"
    ]
  ],
  "submitter": "David Renshaw",
  "commentary": "Found by Elkies - Klagsbrun (2020). A curve of rank exactly 20, via Dujella's elliptic-curve rank-records tables.",
  "created_at": "2026-05-27 22:12:18",
  "updated_at": "2026-07-01 22:30:40"
}