{
  "id": 2892,
  "curve_key": "48269573099158843779223249:-129100207225858034538411836960785145497",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1005616106232475912067151",
    "149421536140955590484679512378606841"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    6
  ],
  "naive_height": 177.41653091241145,
  "faltings_height": 12.843268063994527,
  "conductor": "125026549077672232538730",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "19",
    "23",
    "29",
    "73",
    "97",
    "547",
    "2399",
    "22877"
  ],
  "discriminant": "55439183898058184156721431417927380376370738500793390795068159000976814080",
  "regulator": "530333.2897303543511334272202976885987578935207250196",
  "points": [
    [
      "62603623710",
      "294468440371266861"
    ],
    [
      "-171843292752",
      "-563165401741104555"
    ],
    [
      "81838639761498/961",
      "7560165179333045088027/29791"
    ],
    [
      "6627954227184",
      "-16871541381249849387"
    ],
    [
      "-554612937174690/2209",
      "-64510325175796828854237/103823"
    ],
    [
      "6055399612704264/625",
      "-468717877164630400753587/15625"
    ],
    [
      "-330616454896008/1369",
      "-31150344990726063431145/50653"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z6old678-126, rational kernel x=535079801286. 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 20:27:10",
  "updated_at": "2026-09-26 20:27:10"
}