{
  "id": 74,
  "curve_key": "10360501076277308256728157729703672081:16825848144008099204725392608156810861436365523723401479",
  "ainvs": [
    "1",
    "1",
    "1",
    "-215843772422443922015169952702159835",
    "-19474361277787151947255961435459054151501792241320535"
  ],
  "rank_lower_bound": 21,
  "naive_height": 255.6931918496502,
  "faltings_height": 19.35836145829672,
  "conductor": "26112076915897777815571388664430310998157918697219343275140810790098571234096793308930",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "23",
    "47",
    "4507",
    "115482611374267602141168398241396608699381902319617225736297616061235976719"
  ],
  "discriminant": "479737754043767746536923774462246533556793859277365678757052823009411494064048885744243744500948985175040000",
  "regulator": "1057662683061657998079887.5644599317446350524828508690354387929045294397158378546",
  "points": [
    [
      "800843008889340065933/16",
      "22662214190910903990783584765347/64"
    ],
    [
      "10610541066763914590637/2209",
      "1087744114825178454840094794778034/103823"
    ],
    [
      "907186946780634143",
      "728916386168451830641677698"
    ],
    [
      "196833201085564442194083107/227919409",
      "2277807398930440819587410184793923763894/3440899317673"
    ],
    [
      "185463474139064652528000075/366301321",
      "225699857838583242849473830466481978146/7010640982619"
    ],
    [
      "-12485261071234691432503/123904",
      "1543303353428939982282171752702539/43614208"
    ],
    [
      "-59703014087684747037/361",
      "741881245094154068525036126962/6859"
    ],
    [
      "-73270463404799613067/361",
      "866878137858638792891117943482/6859"
    ],
    [
      "-360733396398627565",
      "106985840484096728947883974"
    ],
    [
      "-389445180957906897",
      "74288355118790673852542098"
    ],
    [
      "-1474458350349858512665407/14205361",
      "2278493401578368084310409028259332632/53540005609"
    ],
    [
      "-114305856035468892691779277/278589481",
      "16972779768877136292841029639987095378/4649937027371"
    ],
    [
      "-21972533600828202797/81",
      "100790786584963504563876005302/729"
    ],
    [
      "-25047938415396324842058977/71216721",
      "68347192566984943007522052612937752062/600997908519"
    ],
    [
      "3434828081885118352213715284707/5137262501809",
      "4279912483838925044234939165329697576812433846/11643877735262694377"
    ],
    [
      "-227656313261676647",
      "133660024327268949095297798"
    ],
    [
      "-4098089434105992137835293/12552849",
      "5660088413991351759301403659890889706/44474744007"
    ],
    [
      "2657828735869178020212617/1495729",
      "4174499731549997186596131721273201376/1829276567"
    ],
    [
      "883965004314243424124994323/850947241",
      "23250077986002214917145041708721276812178/24822981967211"
    ],
    [
      "37543938954172817209003/73441",
      "1224097915991280099903835490020298/19902511"
    ],
    [
      "19165312347502458410162233/17214201",
      "75593839815741485450348997055551694952/71421719949"
    ]
  ],
  "submitter": "David Renshaw",
  "commentary": "Provenance: Nagao-Kouya (1994), “An example of elliptic curve over Q with rank >= 21,” as reproduced in Nagao, “Construction of high-rank elliptic curves.” The paper gives this minimal model y^2 + xy + y = x^3 + x^2 - 215843772422443922015169952702159835*x - 19474361277787151947255961435459054151501792241320535 and 21 independent points. Three point coordinates here use the values from Nagao’s scanned paper rather than the later HTML mirror, whose P2, P12, and P20 appear to contain transcription errors.",
  "created_at": "2026-06-01 14:26:55",
  "updated_at": "2026-07-01 22:29:41"
}