{
  "id": 3947,
  "curve_key": "40198503155492656:-8058321740330897918621696",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-837468815739430",
    "9326761552687403763400"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2,
    2
  ],
  "naive_height": 114.6978184647133,
  "faltings_height": 7.2690577539524375,
  "conductor": "1578385609386038880",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "19",
    "31",
    "71",
    "101",
    "157",
    "281",
    "2521"
  ],
  "discriminant": "12154003312299691040575162140484282726440000",
  "regulator": "1461300336.979617524468990498949013244194569757018608",
  "points": [
    [
      "8234668060609/242064",
      "16929025198893108665/119095488"
    ],
    [
      "190034506408579247585/7737320812816",
      "-1286604861921347953943453282775/21522162522212236864"
    ],
    [
      "38312339447761/774400",
      "-203288298101368825959/681472000"
    ],
    [
      "66024521799049/2304",
      "-536485113054454277285/110592"
    ],
    [
      "2923306409/64",
      "-131905178915445/512"
    ],
    [
      "16646719126409/984064",
      "802785972336439845/976191488"
    ],
    [
      "12359688203502259/375003225",
      "961420372410930264561248/7261937452125"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3664 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 7: 7 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 04:32:02",
  "updated_at": "2026-10-05 04:32:02"
}