{
  "id": 3964,
  "curve_key": "4169963897157433500248256:-3615861483840291775090004897890043904",
  "ainvs": [
    "0",
    "0",
    "0",
    "-86874247857446531255172",
    "4185024865555893258206024187372736"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    2,
    2
  ],
  "naive_height": 170.06984882962294,
  "faltings_height": 12.228742095086295,
  "conductor": "3716012842930786646909643840",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "19",
    "23",
    "37",
    "59",
    "109",
    "137",
    "157",
    "163",
    "199",
    "277",
    "449"
  ],
  "discriminant": "34395471863326763409908678779571360723610636206386854460371585600000000",
  "regulator": "134516945192.29146996902811550424130951477269473974684480",
  "points": [
    [
      "-61426775512903/196",
      "68819495171732140275/2744"
    ],
    [
      "19812449283517073/432964",
      "-4979281222923448068646425/284890312"
    ],
    [
      "58135146620155817/27556",
      "-13882783458958932787771275/4574296"
    ],
    [
      "55310639175297/196",
      "-127002842165180805025/2744"
    ],
    [
      "2834402467553/4",
      "4370261396619524175/8"
    ],
    [
      "-9904282237710255591/41731600",
      "28827965111316387116482206077/269586136000"
    ],
    [
      "-698931050799211047/3247204",
      "664909847064401514134684675/5851461608"
    ],
    [
      "244126245854513/784",
      "-1878900765937051638825/21952"
    ],
    [
      "317336215795647647921/8179600",
      "5652843206201839746772956804969/23393656000"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3678 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 9: 9 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 04:35:31",
  "updated_at": "2026-10-05 04:35:31"
}