{
  "id": 2660,
  "curve_key": "3185227201:-178669825840801",
  "ainvs": [
    "1",
    "0",
    "0",
    "-66358900",
    "206788250000"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    4,
    2
  ],
  "naive_height": 65.64536837436066,
  "faltings_height": 3.3145810481396984,
  "conductor": "681870",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "17",
    "191"
  ],
  "discriminant": "227641658827636236960000",
  "regulator": "2.69524188279579459181578435925299618507240",
  "points": [
    [
      "177872",
      "-75028948"
    ],
    [
      "55540",
      "-12983300"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1188 via the rational 2-torsion point x=-2200. 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 20:16:15",
  "updated_at": "2026-09-26 20:16:15"
}