{
  "id": 3071,
  "curve_key": "-2590671118784:-471248907576855040",
  "ainvs": [
    "0",
    "1",
    "0",
    "53972314975",
    "545444967133759"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    2
  ],
  "naive_height": 85.74881423188809,
  "faltings_height": 5.214966850414857,
  "conductor": "733406508076595441216",
  "bad_primes": [
    "2",
    "17",
    "89",
    "223",
    "257",
    "2503",
    "34897"
  ],
  "discriminant": "-10190719808189110783371071777210368",
  "regulator": "2225382.8597962923078481868897283023205775986800566415020",
  "points": [
    [
      "78717",
      "72675644"
    ],
    [
      "167154",
      "119321083"
    ],
    [
      "305757",
      "213617324"
    ],
    [
      "191013/4",
      "454784057/8"
    ],
    [
      "302394",
      "210992873"
    ],
    [
      "111494947/121",
      "-1214528504944/1331"
    ],
    [
      "6201579",
      "-15454625008"
    ],
    [
      "50869739",
      "-362822154768"
    ],
    [
      "2577005083/6241",
      "-150545191776080/493039"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1372 via the rational 2-torsion point x=5043. 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 20:35:54",
  "updated_at": "2026-09-26 20:35:54"
}