{
  "id": 2801,
  "curve_key": "22173010013601:-104407771232432380401",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-461937708617",
    "120842443299742409"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    6
  ],
  "naive_height": 92.18969070003502,
  "faltings_height": 5.3095702133450535,
  "conductor": "1317390570",
  "bad_primes": [
    "2",
    "3",
    "5",
    "31",
    "43",
    "79",
    "139"
  ],
  "discriminant": "120698679439288764366709824000000",
  "regulator": "63.40840226037998172388202008042309394912504199",
  "points": [
    [
      "393667",
      "-1050884"
    ],
    [
      "19283133/49",
      "-270927362/343"
    ],
    [
      "208791111/529",
      "-29658662476/12167"
    ],
    [
      "-5302923/16",
      "31202745829/64"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1608 via the rational 2-torsion point x=-195705. 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 20:23:04",
  "updated_at": "2026-09-26 20:23:04"
}