{
  "id": 3000,
  "curve_key": "12892971326188486059747106219599841:-1462950114717072446519182942005112210770601677825361",
  "ainvs": [
    "1",
    "0",
    "0",
    "-268603569295593459578064712908330",
    "1693229299441056049976534667502758242071692532900"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    6
  ],
  "naive_height": 235.6259711197405,
  "faltings_height": 17.395579469038235,
  "conductor": "36066743023784036920315345816430",
  "bad_primes": [
    "2",
    "5",
    "7",
    "11",
    "13",
    "19",
    "29",
    "37",
    "47",
    "61",
    "113",
    "131",
    "181",
    "191",
    "211",
    "1543",
    "369983"
  ],
  "discriminant": "1712354480578621378073195764543265928593179857329667367025709630306054586089784169803808768000000",
  "regulator": "8400141.04818399343055091315567196986395242615651457115",
  "points": [
    [
      "11419439062521560",
      "339209428614138189111970"
    ],
    [
      "783071783150077492/81",
      "-4303185666791220981949546/729"
    ],
    [
      "216850812423210330260/22201",
      "128332829667412943213851153230/3307949"
    ],
    [
      "3570824800484402310/361",
      "-441248703802786220335752770/6859"
    ],
    [
      "13813796884486109457940/18601969",
      "98070634559813113801145402609359190/80230292297"
    ],
    [
      "26426599304749082304548340/4299031489",
      "147648202657312726721532142974255847610/281874597639263"
    ],
    [
      "-163527623527207310/9",
      "20476278346300752393101740/27"
    ],
    [
      "23236510292447055220/2401",
      "-1484398647695682069653785370/117649"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z6old678-071, rational kernel x=-74068089074960289/4. 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 20:32:43",
  "updated_at": "2026-09-26 20:32:43"
}