{
  "id": 2577,
  "curve_key": "8305899361:-676113264746641",
  "ainvs": [
    "1",
    "0",
    "0",
    "-173039570",
    "782524080900"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    8
  ],
  "naive_height": 68.52069559697911,
  "faltings_height": 3.6871987362008976,
  "conductor": "249690",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "29",
    "41"
  ],
  "discriminant": "67058993610000000000000000",
  "regulator": "2.372807309150949139520127931941520031558",
  "points": [
    [
      "46660/529",
      "10656963410/12167"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1079 via the rational 2-torsion point x=-76321/4. 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 20:10:25",
  "updated_at": "2026-09-26 20:10:25"
}