{
  "id": 2913,
  "curve_key": "117554312885232830777641:-37743357004617846206234639054631061",
  "ainvs": [
    "1",
    "0",
    "1",
    "-2449048185109017307868",
    "43684440977362864278827303019056"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    6
  ],
  "naive_height": 159.36356225094463,
  "faltings_height": 11.231539764182775,
  "conductor": "4439405348342065911810",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "19",
    "23",
    "29",
    "79",
    "257",
    "523",
    "631",
    "1741"
  ],
  "discriminant": "115696752797146325107688309040926887790253470009441841354155531250",
  "regulator": "69568.28038509566686978346242242977943687837179729251",
  "points": [
    [
      "-109727782502760/2209",
      "679009964953423774361/103823"
    ],
    [
      "-3747231430834041/592900",
      "-3504031222547641336325167/456533000"
    ],
    [
      "1581136020630990/10609",
      "-59742521762738899451936/1092727"
    ],
    [
      "5593803960241466460/177241",
      "-13230015961731509654800338848/74618461"
    ],
    [
      "1262121443071260",
      "-44838566927104430161568"
    ],
    [
      "141754883355/4",
      "-9468909878808469/8"
    ],
    [
      "52357694878260",
      "-378852897294737672693"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1265 via the rational 2-torsion point x=28368135073. Independent witness points are the images of that curve's witnesses under 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 20:28:06",
  "updated_at": "2026-09-26 20:28:06"
}