{
  "id": 2564,
  "curve_key": "243553:109360495",
  "ainvs": [
    "1",
    "1",
    "1",
    "-5074",
    "-128689"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    2,
    2
  ],
  "naive_height": 37.209269570874135,
  "faltings_height": 1.069400962759865,
  "conductor": "966",
  "bad_primes": [
    "2",
    "3",
    "7",
    "23"
  ],
  "discriminant": "1439452851984",
  "regulator": "2.429046614030699609497398526925843435269",
  "points": [
    [
      "131",
      "-1281"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#2078 via the rational 2-torsion point x=25. 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 20:09:31",
  "updated_at": "2026-09-26 20:09:31"
}