{
  "id": 36,
  "curve_key": "-1647274302837199025396910363003835619879:-2751301637983405898417110838514633830651832727715466959927581",
  "ainvs": [
    "1",
    "0",
    "1",
    "34318214642441646362435632562579908747",
    "3184376895814127197244886284686214848599453811643486936756"
  ],
  "rank_lower_bound": 15,
  "naive_height": 278.33435940448464,
  "faltings_height": 21.2523609564019,
  "conductor": "8754566324589342390719388201154487417353298842735433399274068130",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "17",
    "67",
    "89",
    "139",
    "211",
    "281",
    "431",
    "443",
    "577",
    "647",
    "977",
    "1613",
    "3863",
    "10567",
    "11923",
    "15361",
    "73277"
  ],
  "discriminant": "-4383177432172452900429407516665453934052428354033391150708350854907555007169944896851345195235905604109325415039062500",
  "regulator": "26441299746981574.028361312934843803735096979068358730331594461979348",
  "points": [
    [
      "-5955399047526089895",
      "-52619192486073556789679851928"
    ],
    [
      "4996845231479851005",
      "58996807068911558580932032822"
    ],
    [
      "-13155206566829859045",
      "-21360729170232157127198638028"
    ],
    [
      "5982316535030750730",
      "60031451151089353115173694947"
    ],
    [
      "3520990345094746477605",
      "208928587539794577855401843236822"
    ],
    [
      "-149780582516304339030/289",
      "-276460561394858085500066301116014/4913"
    ],
    [
      "5537764707520796477505/256",
      "485495189997228202630782626087287/4096"
    ],
    [
      "10379720384859947873670/529",
      "1299762167535132813050160826170149/12167"
    ],
    [
      "3607902715536254330407755/36481",
      "6876286874413935169019164791798028712/6967871"
    ],
    [
      "575451914344737045120/18769",
      "145126149873708232941281933935318916/2571353"
    ],
    [
      "-635343181823720560310/81",
      "-35955391603910411255538526302302/729"
    ],
    [
      "385275433846822770303250/9",
      "239142619084196570639847351097336094/27"
    ],
    [
      "11630065797764473356485380/349281",
      "41921913401808378926412528792277717237/206425071"
    ],
    [
      "2130862087205394565011555/206116",
      "6377017660319811010371576798520557433/93576664"
    ],
    [
      "361886218060793196368152192851/82159049956",
      "1377397812507014979022748799194701395570639671/23549577125088104"
    ]
  ],
  "submitter": "David Renshaw",
  "commentary": "Found by Dujella (2002). A curve of rank exactly 15, via Dujella's elliptic-curve rank-records tables.",
  "created_at": "2026-05-27 22:12:14",
  "updated_at": "2026-07-01 22:43:36"
}