{
  "id": 2946,
  "curve_key": "16440828691513494975436078243448128614969601:-129207887258257454466378780549792543235291891427624042896152766849",
  "ainvs": [
    "1",
    "0",
    "0",
    "-342517264406531145321584963405169346145200",
    "149546165808168350076798749197633417815774001516503322573183232"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    6
  ],
  "naive_height": 299.84856699000125,
  "faltings_height": 23.03153673622382,
  "conductor": "220989850677256034459433715825098922710",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "17",
    "23",
    "41",
    "73",
    "79",
    "109",
    "163",
    "911",
    "1609",
    "22651",
    "428083",
    "2206483"
  ],
  "discriminant": "-7089530203447088933947656724816219616634747166497758236612542854135787590504504040311532788195124822601318359375000000000000000",
  "regulator": "1692043771.69176290219930430312909693718418370472719238",
  "points": [
    [
      "65648499187634578321978696/85849",
      "460245050804961810135240187555909683536/25153757"
    ],
    [
      "149720261173924935535483649504/243391201",
      "49743963291846902957520308683001218512404048/3797146126801"
    ],
    [
      "630319842134658324704",
      "13567563052296719979832552397648"
    ],
    [
      "-2053365270938642401853536/73441",
      "-251040716467915501848891376861136345872/19902511"
    ],
    [
      "574924369459930197004",
      "-11943994824662679066680727739052"
    ],
    [
      "194299636158527022299175296/196249",
      "2429496924351087763674547200197451421936/86938307"
    ],
    [
      "-80562075463080071840551353056/111957561",
      "-5733292040643182024031457607327275254157232/1184622952941"
    ],
    [
      "110521636242992421156276232336/87179569",
      "-34079321364608354746789273823529575013045296/813995635753"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z6old678-080, rational kernel x=369145749764614618976. 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 20:29:35",
  "updated_at": "2026-09-26 20:29:35"
}