{
  "id": 4004,
  "curve_key": "341896208954634715463838961:-111769936997076007574172987241299766603465",
  "ainvs": [
    "1",
    "0",
    "0",
    "-7122837686554889905496645",
    "129363353005874415196596707510678901441"
  ],
  "rank_lower_bound": 14,
  "torsion": [
    2
  ],
  "naive_height": 189.03452250296294,
  "faltings_height": 13.810707264264284,
  "conductor": "52730095526316529723237209878616107447931486",
  "bad_primes": [
    "2",
    "3",
    "7",
    "17",
    "23",
    "31",
    "37",
    "43",
    "53",
    "59",
    "73",
    "211",
    "601",
    "36697",
    "78193",
    "10736721060361"
  ],
  "discriminant": "-7206338852272152955943343901355807894035042958187391355226664806656748760885248",
  "regulator": "214971018090307181044.003195070717263874792759139615255871228229541",
  "points": [
    [
      "6229204281160469554/27889",
      "15546060781388961387032803553/4657463"
    ],
    [
      "-4435182696443642/3721",
      "2648586501949843243452439/226981"
    ],
    [
      "-236111804650709638988880674/43193668251721",
      "632172839240857704927913170872077079627/283876951353609987269"
    ],
    [
      "-144670048504430492569412/56206452241",
      "152308919334535422292726276887172081/13325369490844039"
    ],
    [
      "-19061254165186208807/15555136",
      "716113007904836147167884185351/61349456384"
    ],
    [
      "308236644486857332213/119333776",
      "14759992215023361711578853011977/1303602169024"
    ],
    [
      "1607917652714422096978/199628641",
      "68773849172143002168608851483127/2820553068689"
    ],
    [
      "16589962026551328408658666/265792833601",
      "67528388656231667405513072261825116033/137029761155829151"
    ],
    [
      "281546516145516190176056254/32459945153769",
      "4962776562444903162103338247249681058597/184936090501112811147"
    ],
    [
      "-2959007122999702344287318/691686632329",
      "5194693796422837991348499549809444819/575259863315485733"
    ],
    [
      "-34179131344983491726069412/8846692486921",
      "262094096036648495739188419994317213821/26313062484856120219"
    ],
    [
      "476787352276748997998086334806/54103815543948361",
      "344866511956805191107960699055944597906571847/12584670257079857987431109"
    ],
    [
      "81430378301370943562912394106/352386519785521",
      "23235550921920180559753534147841434756127023/6614986006339528576681"
    ],
    [
      "-1912361860674979242803534414/395705150890921",
      "56165402501908985260630330070608360257677/7871501005568352554219"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3642 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 14: 14 independent points certified by the unchanged ICARM verifier, with a matching unconditional upper bound computed using PARI/GP 2.17.2 ellrank. This is an additional representative of a known isogeny class, not a claim of a new world rank record.",
  "created_at": "2026-10-05 04:43:57",
  "updated_at": "2026-10-05 04:43:57"
}