{
  "id": 2862,
  "curve_key": "10056546485507809:-1008402957017259567006673",
  "ainvs": [
    "1",
    "0",
    "0",
    "-209511385114746",
    "1167133034644027591140"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    6
  ],
  "naive_height": 110.54100062683551,
  "faltings_height": 6.904181876850365,
  "conductor": "6110680457310",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "67",
    "73",
    "181",
    "1609"
  ],
  "discriminant": "106208269421099600009675852422943283302400",
  "regulator": "328.790982145967766851911790978053816684498448048",
  "points": [
    [
      "21155784",
      "78751027446"
    ],
    [
      "-6411756",
      "47404447350"
    ],
    [
      "452953722/49",
      "-1547812945692/343"
    ],
    [
      "77243452/9",
      "-29492552518/27"
    ],
    [
      "3076147140/361",
      "-5235148040430/6859"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1674 via the rational 2-torsion point x=-4210796. 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 20:25:48",
  "updated_at": "2026-09-26 20:25:48"
}