{
  "id": 2662,
  "curve_key": "5234078593:23594716773055",
  "ainvs": [
    "1",
    "1",
    "1",
    "-109043304",
    "-27354134679"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    4,
    2
  ],
  "naive_height": 67.13536997039844,
  "faltings_height": 3.662618313218326,
  "conductor": "659022",
  "bad_primes": [
    "2",
    "3",
    "7",
    "13",
    "17",
    "71"
  ],
  "discriminant": "82658507783312370783654144",
  "regulator": "11.6407403859762630711447686822206296024438",
  "points": [
    [
      "1185853/49",
      "1159463915/343"
    ],
    [
      "232909/16",
      "-78066685/64"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1471 via the rational 2-torsion point x=5157. 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 20:16:28",
  "updated_at": "2026-09-26 20:16:28"
}