{
  "id": 2781,
  "curve_key": "46824945703849:-320417177567854521493",
  "ainvs": [
    "1",
    "0",
    "1",
    "-975519702164",
    "370853133484300886"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    6
  ],
  "naive_height": 94.43231161410985,
  "faltings_height": 5.410394364242402,
  "conductor": "3637272210",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "23",
    "191",
    "193"
  ],
  "discriminant": "36423277217282109926428927627500",
  "regulator": "64.77021721277704136819405362812158091096843604",
  "points": [
    [
      "21900333/16",
      "-80998835573/64"
    ],
    [
      "36584457/64",
      "-1063184209/512"
    ],
    [
      "570609",
      "-631547"
    ],
    [
      "683631",
      "-153487523"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1610 via the rational 2-torsion point x=-284991. 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 20:22:09",
  "updated_at": "2026-09-26 20:22:09"
}