{
  "id": 2706,
  "curve_key": "7389552696976:19573360606321235776",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-153949014520",
    "-22654301237274368"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    4,
    2
  ],
  "naive_height": 88.8932649627221,
  "faltings_height": 5.315300810978362,
  "conductor": "922220880",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "23",
    "29",
    "823"
  ],
  "discriminant": "11801905982734382614627969311360000",
  "regulator": "109.43882875946963408820599383823040233452378",
  "points": [
    [
      "-9690964/49",
      "2588648460/343"
    ],
    [
      "-24551423/121",
      "20140533756/1331"
    ],
    [
      "7782381/4",
      "-21230258665/8"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1571 via the rational 2-torsion point x=511025. 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 20:18:36",
  "updated_at": "2026-09-26 20:18:36"
}