{
  "id": 2945,
  "curve_key": "-23060130931962182027721335392502757701039:-10121955025971941553979767179118868693874959848743509306862041",
  "ainvs": [
    "1",
    "0",
    "0",
    "480419394415878792244194487343807452105",
    "11715225724504561983812913629070384220968219735916971578025"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    6
  ],
  "naive_height": 280.9396248184579,
  "faltings_height": 21.481914379828122,
  "conductor": "1041840789186569790031551162756230429730",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "23",
    "31",
    "37",
    "41",
    "43",
    "47",
    "61",
    "67",
    "107",
    "151",
    "167",
    "199",
    "587",
    "1181",
    "613667"
  ],
  "discriminant": "-66386950833066730499892908623042282494252906337179088693609537500582290865032835849655240215224426941940274197607936000",
  "regulator": "316058352.724029503011820555727648868697696765573285054",
  "points": [
    [
      "12564125617806673607830/169",
      "1487373900716243593804898382690025/2197"
    ],
    [
      "39705014395620169110144682/1692601",
      "417194478284574162006261349439691156281/2202073901"
    ],
    [
      "-100734366653147000414550/11881",
      "-108600645449747251423478525259433155/1295029"
    ],
    [
      "-1522723274112636721467290/657721",
      "54893674053262778714178969444806823535/533411731"
    ],
    [
      "3258276462809291489878/49",
      "-199318132348444329750369538802909/343"
    ],
    [
      "-1051881197304195519918890/579121",
      "-45877638313132337367542444157250866595/440711081"
    ],
    [
      "-941909350291879569087378709364314365241002410/59132510384268358546407889",
      "-2092288103915975204450210742549518897182311232550307145124840308435/454715203410890756201500198868967378713"
    ],
    [
      "8968061481997083931092388150/196249",
      "849274169762404314069142119694379670580415/86938307"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z6old678-035, rational kernel x=127566650300506323791/4. 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 20:29:31",
  "updated_at": "2026-09-26 20:29:31"
}