{
  "id": 2677,
  "curve_key": "13888:-166400",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-289",
    "289"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    2,
    2
  ],
  "naive_height": 28.616341310700395,
  "faltings_height": 0.452304599261751,
  "conductor": "3264",
  "bad_primes": [
    "2",
    "3",
    "17"
  ],
  "discriminant": "1534132224",
  "regulator": "2.45090362517594440325204525216302401805645",
  "points": [
    [
      "145",
      "-1728"
    ],
    [
      "19",
      "-36"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1426 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 20:17:18",
  "updated_at": "2026-09-26 20:17:18"
}