{
  "id": 2982,
  "curve_key": "-7043619678971726622742592792477471951:-147962429452778037049251636053808871540366952816695016233",
  "ainvs": [
    "1",
    "0",
    "0",
    "146742076645244304640470683176613999",
    "171252811866641246597010492560493589669538011580337065"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    6
  ],
  "naive_height": 258.67310681633427,
  "faltings_height": 19.61608613146401,
  "conductor": "57726875537107193277056539769346690",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "17",
    "19",
    "23",
    "29",
    "53",
    "67",
    "167",
    "2333",
    "17257811",
    "4858141109"
  ],
  "discriminant": "-12871720290263634455969455343510682632604566330477917509582790341664816855244070837762797640831190318285946880",
  "regulator": "3933080732.56272951717968151581607049424469672567597957",
  "points": [
    [
      "20246611501315634474/49",
      "188628636373967199227078072237/343"
    ],
    [
      "67364116443960568085992714/132687361",
      "937972134948179671815826725756402730469/1528425711359"
    ],
    [
      "299848941253355186",
      "-492150894549056720640386965"
    ],
    [
      "-3725859169263175334/9",
      "5369809936111231178308088857/27"
    ],
    [
      "772432896085059194",
      "863409113895994772051526011"
    ],
    [
      "2782658504078870117308187174/366301321",
      "147002906747320354044358067005539209194909/7010640982619"
    ],
    [
      "175144501334329855586/121",
      "-2460149622899655462904680351791/1331"
    ],
    [
      "3201605622908104410994/3969",
      "225666961851886083984574947407005/250047"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z6old678-026, rational kernel x=234046202231251658. Source: https://dujella.github.io/tors/z6old678.html. Independent witness points transported by the degree-2 isogeny. Witnesses saturated by exact rational halves of published and transported relations; quadratic-character independence is certified.",
  "created_at": "2026-09-26 20:31:46",
  "updated_at": "2026-09-26 20:31:46"
}