{
  "id": 2823,
  "curve_key": "660773034719056:-15539633696417085695296",
  "ainvs": [
    "0",
    "1",
    "0",
    "-13766104889980",
    "17985682559929256228"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    6
  ],
  "naive_height": 102.3732945908384,
  "faltings_height": 6.496867827797897,
  "conductor": "16804238845740",
  "bad_primes": [
    "2",
    "3",
    "5",
    "19",
    "61",
    "109",
    "241",
    "9199"
  ],
  "discriminant": "27214797469729973331075006622082076000000",
  "regulator": "2481.30125823846221413258617894477540762216758632",
  "points": [
    [
      "1534851104/529",
      "-19119159779850/12167"
    ],
    [
      "865221029/4",
      "-25446443220225/8"
    ],
    [
      "138256911476/151321",
      "146223966948774390/58863869"
    ],
    [
      "-2512924",
      "6058901250"
    ],
    [
      "97560392561/4096",
      "-30121197199979145/262144"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1666 via the rational 2-torsion point x=-1316976. 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 20:24:03",
  "updated_at": "2026-09-26 20:24:03"
}