{
  "id": 2955,
  "curve_key": "1652037157902122275555082249414438500874641:-2123387812067644096636346979717346296046585178431834586351365561",
  "ainvs": [
    "1",
    "0",
    "0",
    "-34417440789627547407397546862800802101555",
    "2457624782485699185918829773125570732214412679464945519213025"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    6
  ],
  "naive_height": 291.6317492198177,
  "faltings_height": 21.869425217969546,
  "conductor": "18307122213101568954344266175402433870",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "17",
    "19",
    "23",
    "29",
    "37",
    "41",
    "47",
    "97",
    "107",
    "757",
    "853",
    "2617",
    "97787",
    "300823"
  ],
  "discriminant": "4767212599777757543010186977076106578723060088734486134205495438837312845356723252956316145877942661041220384456704000",
  "regulator": "93413263.7656408709031993613994845532823710569575340500",
  "points": [
    [
      "50910570112336707648866270/452929",
      "-29156994082994374365423422983802281975/304821217"
    ],
    [
      "42433066738459940211956/25",
      "-8690749576983011914094952110460569/125"
    ],
    [
      "427781364384108126623/4",
      "20281327900229293774692970693/8"
    ],
    [
      "106882408849824018382",
      "3786590476454677500265829401"
    ],
    [
      "-91321154163838552114",
      "2199792621072654908554802578457"
    ],
    [
      "62765599966051461747045997730/533656201",
      "2358957744570844141668241033525918463219045/12327991899301"
    ],
    [
      "84660944818439003522530526/2627641",
      "5007588940901147337194534008292006521637/4259406061"
    ],
    [
      "131379669704137296634375892030/335146249",
      "-43038515785458801609828093619450463282399965/6135522380443"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z6old678-099, rational kernel x=-857545932178525503089/4. 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 20:29:58",
  "updated_at": "2026-09-26 20:29:58"
}