{
  "id": 3969,
  "curve_key": "95986402600104048808644350400:-21004341736126180434010380799759046222208000",
  "ainvs": [
    "0",
    "0",
    "0",
    "-1999716720835501016846757300",
    "24310580713109005131956459258980377572000"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    2,
    2
  ],
  "naive_height": 200.20201215807896,
  "faltings_height": 14.710892057494663,
  "conductor": "1213220854870659463310025004843200",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "19",
    "29",
    "37",
    "41",
    "79",
    "83",
    "127",
    "131",
    "163",
    "191",
    "433",
    "853",
    "883"
  ],
  "discriminant": "256468599864180747848196024749326478809810189753372342845504131166600954177600000000",
  "regulator": "148951370174809.0572729585216845196351676563743242540027773",
  "points": [
    [
      "8451368116133006/80089",
      "-3518551278181779695130150304/22665187"
    ],
    [
      "2084528927425108585/1478656",
      "263610242546067720184894291125/1798045696"
    ],
    [
      "169915083679630578936910/4644286201",
      "-3470962146189557391874319104980000/316503460311949"
    ],
    [
      "50965325423068585/7056",
      "-59987693666590690291152875/592704"
    ],
    [
      "115145766418757649849401/578979844",
      "38133935845947316814398524435750451/13931413006328"
    ],
    [
      "15065813672843146121/309136",
      "35478079622315680931779219931/171879616"
    ],
    [
      "1000563484699084724387785/84200950276",
      "-1152712971386752587920432335030894875/24432926545388024"
    ],
    [
      "7269925345205522104965826663390/93647520030305329",
      "16634303831241475909895807243240241415125996000/28657903856542961111207767"
    ],
    [
      "25461287055987325882767310/679010608441",
      "-25335248244384743193790458617903028000/559519000578161261"
    ],
    [
      "23428695240547411481087710/11107262881",
      "-113377035596240647397521938206463462000/1170605542291471"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3697 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 10: 10 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 04:36:31",
  "updated_at": "2026-10-05 04:36:31"
}