{
  "id": 2957,
  "curve_key": "3482833117177354814771765045957088219081:-216162187138222670257397723923092474259544429775746939574021",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-72559023274528225307745105124106004564",
    "250187716595165127630868602951840938571779366299252125648"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    6
  ],
  "naive_height": 273.2467585859326,
  "faltings_height": 20.708507039695757,
  "conductor": "15589465171966572283635649128662490",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "19",
    "29",
    "31",
    "43",
    "73",
    "97",
    "109",
    "197",
    "379",
    "2609",
    "6451",
    "157177"
  ],
  "discriminant": "-2591947211593298640086445789020175942365978164170711218040327927623437392486629702829194693418026874023437500000000",
  "regulator": "152581484.222777937762113774076100618112074853687919715",
  "points": [
    [
      "144739503549353795688/49",
      "2692745695530420000485594385492/343"
    ],
    [
      "8136391552125116115872893617/2406589249",
      "778829292125264681660285574711248087616348/118060048788193"
    ],
    [
      "-8292715268854878063",
      "-16781425775370101655920913156"
    ],
    [
      "285681729902787075909573/4624",
      "-151318104186508588359765061038885267/314432"
    ],
    [
      "4420713064358286312",
      "-3977157447235811945629143156"
    ],
    [
      "9931308566006705256084267/279841",
      "-30472695997458223420779416600963338809/148035889"
    ],
    [
      "5460411138377800312",
      "-4098014956896064516007953156"
    ],
    [
      "512191852505990685000167835768/92892677089",
      "-119255196663200524617731801689751479504394172/28312108801216687"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z6old678-100, rational kernel x=79135743506933709507/4. 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 20:30:05",
  "updated_at": "2026-09-26 20:30:05"
}