{
  "id": 2816,
  "curve_key": "-506036594950839:-2862296731334223963909",
  "ainvs": [
    "1",
    "-1",
    "0",
    "10542429061476",
    "3312840803436975330"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    6
  ],
  "naive_height": 101.5728903139144,
  "faltings_height": 6.537442547082726,
  "conductor": "40432009593690",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "31",
    "47",
    "463",
    "4657"
  ],
  "discriminant": "-79730942989378299159250444046708159156250",
  "regulator": "27055.8295459624520820240632525769466306093587785",
  "points": [
    [
      "159314179/9",
      "2044758220744/27"
    ],
    [
      "-3760979/16",
      "58023331433/64"
    ],
    [
      "3075000049/625",
      "206233500342482/15625"
    ],
    [
      "15235596109/5625",
      "3033942620527498/421875"
    ],
    [
      "1738178647519/208849",
      "-2466357051349313179/95443993"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1667 via the rational 2-torsion point x=155688. 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 20:23:44",
  "updated_at": "2026-09-26 20:23:44"
}