{
  "id": 2895,
  "curve_key": "16220775918443254868672361:-64148813439096628122371282263182177141",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-337932831634234476430674",
    "74246311850890765756949394571864818"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    6
  ],
  "naive_height": 174.14500534962662,
  "faltings_height": 12.403567609178078,
  "conductor": "407739781740207625175610",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "17",
    "19",
    "29",
    "41",
    "67",
    "101",
    "997",
    "2141",
    "5711"
  ],
  "discriminant": "88446769142052957460258866900721611612535160889447862321633607172122250",
  "regulator": "15265377.06014232454133121820671946126920781571633710",
  "points": [
    [
      "23868291739441/64",
      "4799688346055860717/512"
    ],
    [
      "405550431229",
      "62440593046962116"
    ],
    [
      "377778392347",
      "22311357692377334"
    ],
    [
      "394436322937",
      "48163446052843304"
    ],
    [
      "89228465644117",
      "842841517319867492159"
    ],
    [
      "416690592397",
      "76047835962924084"
    ],
    [
      "-3719816798246984583/13476241",
      "18934924494491225996678129544/49471280711"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z6old678-122, rational kernel x=-185908156668. 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 20:27:18",
  "updated_at": "2026-09-26 20:27:18"
}