{
  "id": 2567,
  "curve_key": "448:-8704",
  "ainvs": [
    "0",
    "1",
    "0",
    "-9",
    "7"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    2
  ],
  "naive_height": 18.314379697244956,
  "faltings_height": -0.5098561454222533,
  "conductor": "128",
  "bad_primes": [
    "2"
  ],
  "discriminant": "8192",
  "regulator": "0.2161655822867590162580377816961518488022",
  "points": [
    [
      "-1",
      "4"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1795 via the rational 2-torsion point x=-1. 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 20:09:45",
  "updated_at": "2026-09-26 20:09:45"
}