{
  "id": 2995,
  "curve_key": "-133766249054292619301514937638614591:-208002378993245239185733441439104284168635110904640673",
  "ainvs": [
    "1",
    "0",
    "0",
    "2786796855297762902114894534137804",
    "240743494205144952993498628495999089260309626577040"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    6
  ],
  "naive_height": 245.53877851959953,
  "faltings_height": 18.525820911764562,
  "conductor": "872082441667970380560815798196270",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "17",
    "19",
    "23",
    "59",
    "67",
    "97",
    "139",
    "283",
    "6673",
    "7417",
    "68071609"
  ],
  "discriminant": "-26422756900008729269167737768832523043639039850408083788459941994277902784459288073316528468195888640000",
  "regulator": "1288921605.29204913961482347719344906696197417403632380",
  "points": [
    [
      "-44489218886122442",
      "5357610152250217904461096"
    ],
    [
      "1184800050303888552/169",
      "-35468135772553303018122939588/2197"
    ],
    [
      "25649756154191010531076/189225",
      "4589750560978766838163586206352096/82312875"
    ],
    [
      "135620725224439269448/3481",
      "-4150769053981794724666084068316/205379"
    ],
    [
      "2361837048608695735552/18769",
      "130711126029938156877768376786988/2571353"
    ],
    [
      "106973264834766184",
      "41987869729929137582229196"
    ],
    [
      "17053199443056312784",
      "70422412414350208849070176420"
    ],
    [
      "-1184719070202218699403399842/35324826601",
      "-69492948462621391357003910783021032202446/6639265834831349"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z6old678-029, rational kernel x=23812609303061224. 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 20:32:32",
  "updated_at": "2026-09-26 20:32:32"
}