{
  "id": 2887,
  "curve_key": "327850618800276022028585569:-6870302276550397272585916365326915507473",
  "ainvs": [
    "1",
    "0",
    "0",
    "-6830221225005750458928866",
    "7951738746006835065576060128812352580"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    6
  ],
  "naive_height": 183.45605346306394,
  "faltings_height": 13.275561705713159,
  "conductor": "1310089338214953805719210",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "29",
    "131",
    "397",
    "887",
    "5527",
    "5900281"
  ],
  "discriminant": "-6922275751026239675846050387723954694055305498717215741367332020102555402240",
  "regulator": "18348579.86860863238398632084634948259601657499946941",
  "points": [
    [
      "1678322292964",
      "1102662708145815886"
    ],
    [
      "-309003411998467604/3728761",
      "-21013337255711218876520227990/7200237491"
    ],
    [
      "219065180327962420/124609",
      "51625598263637254620971390/43986977"
    ],
    [
      "-1568919454865180/9409",
      "-2751072362238009729942770/912673"
    ],
    [
      "21675497412008836/10201",
      "1794069310226596935820310/1030301"
    ],
    [
      "127289886854656/529",
      "30592584718031968464062/12167"
    ],
    [
      "98645308763091499/100",
      "-30982263217926012007562213/1000"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z6old678-132, rational kernel x=1534675231588. 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 20:26:55",
  "updated_at": "2026-09-26 20:26:55"
}