{
  "id": 2975,
  "curve_key": "24804494832860094509279149369157774656:-123308545453073427094976265859718584341388520632139550304",
  "ainvs": [
    "0",
    "1",
    "0",
    "-516760309017918635609982278524120305",
    "142718223904020170076561686183516223710316694927306600"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    6
  ],
  "naive_height": 258.3122646833835,
  "faltings_height": 19.32234309758475,
  "conductor": "665963354664280732450924737051124420",
  "bad_primes": [
    "2",
    "5",
    "11",
    "13",
    "17",
    "19",
    "29",
    "31",
    "37",
    "43",
    "59",
    "83",
    "107",
    "241",
    "331",
    "2791",
    "5569",
    "775811"
  ],
  "discriminant": "32575015906842150197896809944442432316557689780691259221102269739783892007353014625766107664197894531250000",
  "regulator": "940008349.199408383241450826490995796143693898203051789",
  "points": [
    [
      "1566608531261812280155528985/2200735744",
      "-38015261196339997853077468461057898671875/103240915222528"
    ],
    [
      "302152447127281940",
      "119009127290696087163306250"
    ],
    [
      "388728511380880145",
      "24072130062236555589890795"
    ],
    [
      "401066653121200510580/2209",
      "24322087545845325904709740458110/103823"
    ],
    [
      "981581068436218661494740/1692601",
      "-429670591446758365231318992954153050/2202073901"
    ],
    [
      "1248776912503350255582885/2172676",
      "-604069463380503445413212187025720345/3202524424"
    ],
    [
      "8629255649438874891069/22201",
      "79807176248612274033025261922855/3307949"
    ],
    [
      "19565338224391758635/49",
      "2188330219781126555041213475/343"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z6old678-058, rational kernel x=-800777005254988881. 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 20:31:19",
  "updated_at": "2026-09-26 20:31:19"
}