{
  "id": 2965,
  "curve_key": "11082908219599123866296213341374714929761:-1767400137968876043437820153118275451871183940630102627924241",
  "ainvs": [
    "1",
    "0",
    "0",
    "-230893921241648413881171111278639894370",
    "2045602011538050976181939572672311071842291227567176568900"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    6
  ],
  "naive_height": 277.44923039561536,
  "faltings_height": 21.15104348461035,
  "conductor": "2023481314997324610295365836962841490",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "19",
    "31",
    "47",
    "53",
    "61",
    "89",
    "103",
    "181",
    "233",
    "311",
    "491",
    "8252112961"
  ],
  "discriminant": "-1019895925683278214944001291433644074444447196817683271647279897510218644995843142801831742809683783212112719071296000",
  "regulator": "3585249174.44618690773625251153066683381659037966208019",
  "points": [
    [
      "-704405305750855320019380/38809",
      "122535991127977320756609388044059790/7645373"
    ],
    [
      "-20616008069758170287567083098/8576797321",
      "-40398181809257905679455705038411324854542344/794305776695131"
    ],
    [
      "-2711924026335295333380/529",
      "-676834334416005785302653348284670/12167"
    ],
    [
      "10470341702715426252",
      "27855106510504734431583161262"
    ],
    [
      "41478515895255018604866912/410881",
      "-264362407089879352329742020838604470098/263374721"
    ],
    [
      "-2658714628719404370899658652890/148148779801",
      "-1153737046571190561739285169733375621566074470/57022613494184701"
    ],
    [
      "-10106706740325723389626812268/1933272961",
      "-4740293897188215182430618975563531669944642/85004078822209"
    ],
    [
      "54181532059987767851127638073583917883939523064/5349278135513471920537643689",
      "-10686356845797347697601337879351732565779993352931571486506134378967806/391239566844017838513203719330927198239637"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z6old678-024, rational kernel x=9240887879951959140. 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 20:30:40",
  "updated_at": "2026-09-26 20:30:40"
}