{
  "id": 2917,
  "curve_key": "409636188716057753769929281:-8290819730420833893785852209828957876321",
  "ainvs": [
    "1",
    "0",
    "0",
    "-8534087264917869870206860",
    "9595856169467846573498585790738776600"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    6
  ],
  "naive_height": 183.8319349591116,
  "faltings_height": 12.779410938518296,
  "conductor": "4290426777866593139490",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "17",
    "23",
    "29",
    "31",
    "41",
    "101",
    "113",
    "373",
    "16301"
  ],
  "discriminant": "532499342632862238402671218475882427778741806843164167261144894875000",
  "regulator": "809286.4463014778205860048592882970027327610215182760",
  "points": [
    [
      "1722615431570",
      "-81250757342004910"
    ],
    [
      "2286630502310",
      "1427447255757189590"
    ],
    [
      "1688190716366",
      "-3519647137227298"
    ],
    [
      "1641202994968526/961",
      "-1422623481048758664148/29791"
    ],
    [
      "1694063356370",
      "-16748607103426660"
    ],
    [
      "83121758894570/49",
      "-7521783564329465530/343"
    ],
    [
      "26982105516245/16",
      "30614295287207885/64"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z6old678-129, rational kernel x=-843254960680. 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 20:28:18",
  "updated_at": "2026-09-26 20:28:18"
}