{
  "id": 2983,
  "curve_key": "39800566648109582493731934683843197809:-250940462217850758924968652446164376544377683898599937673",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-829178471835616301952748639246733288",
    "290440349789179119333415743475298029821957627286914731"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    6
  ],
  "naive_height": 259.7308334920931,
  "faltings_height": 19.39968275470525,
  "conductor": "279518233526010740846353904622630",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "17",
    "29",
    "31",
    "37",
    "59",
    "67",
    "71",
    "101",
    "109",
    "137",
    "157",
    "331",
    "677",
    "2579"
  ],
  "discriminant": "44195162062651873570853949323245089183220239193598113991095773955965982190351727346615993053191916328550400",
  "regulator": "16088966.2005044102984960496513716516788480001488705707",
  "points": [
    [
      "5467360413203851896122109/10195249",
      "-12310033074503954543458870065882911/32553430057"
    ],
    [
      "14786236441032287237349/26569",
      "-159032130137384990559939583230221/4330747"
    ],
    [
      "2722531763216899927671/3025",
      "86961227433921627806549639001241/166375"
    ],
    [
      "-23688658781097188585715/101761",
      "22274722978835723289599657255912263/32461759"
    ],
    [
      "2763283742551687245",
      "-4370228026214791828939132103"
    ],
    [
      "-92195778694216032330555/109561",
      "22714172299787630101931808528924187/36264691"
    ],
    [
      "108967738861716748534498245/510895609",
      "4054725718042739814561331794280485401659/11547773450227"
    ],
    [
      "1787345929950214088169177045/1710897769",
      "-53162625987125472676454562237627994032781/70767864419147"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z6old678-054, rational kernel x=-257564734993073139. 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 20:31:50",
  "updated_at": "2026-09-26 20:31:50"
}