{
  "id": 3008,
  "curve_key": "4162695208529514487128803599420624:-268564191613049968140940231737504140463554682029632",
  "ainvs": [
    "0",
    "1",
    "0",
    "-86722816844364885148516741654596",
    "310838184737326323107371505278260668623533663780"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    6
  ],
  "naive_height": 232.23441245986342,
  "faltings_height": 17.013878199093533,
  "conductor": "13260845337120940680039952567380",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "17",
    "19",
    "23",
    "31",
    "43",
    "47",
    "53",
    "61",
    "79",
    "257",
    "631",
    "10861",
    "13709"
  ],
  "discriminant": "2655243965401917160766341002763671876064796000909864343890276036071902494340665910826417478400",
  "regulator": "14385630.3769752887910293525879663204214280205065687288",
  "points": [
    [
      "2585749904949138242424/477481",
      "-1255426617235037848426105118454/329939371"
    ],
    [
      "29732884949891274720/5329",
      "10011435206474365021932726390/389017"
    ],
    [
      "36315257685071045/4",
      "-4170892928546548081347855/8"
    ],
    [
      "8254810966628784",
      "-396807588639680488547574"
    ],
    [
      "68372388845627144788172868/12590410849",
      "-8615221114747317592207174493488487850/1412732230133743"
    ],
    [
      "5350566321656256",
      "1005178224707961592134"
    ],
    [
      "5131059697446577880767099669334093318367765273912/609942635079647122985874187347481",
      "-6330713866726629037346818008487379445507679697071759726113592616950922010/15063763459416929189759159086893604838729733194371"
    ],
    [
      "5293514459761536",
      "10041504928525830200826"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z6old678-094, rational kernel x=-2675901289983228. 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 20:33:05",
  "updated_at": "2026-09-26 20:33:05"
}