{
  "id": 2767,
  "curve_key": "400144:-258286528",
  "ainvs": [
    "0",
    "1",
    "0",
    "-8336",
    "296164"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    2
  ],
  "naive_height": 38.7391602005972,
  "faltings_height": 1.1241020916692974,
  "conductor": "7598320",
  "bad_primes": [
    "2",
    "5",
    "17",
    "37",
    "151"
  ],
  "discriminant": "-1529389849600",
  "regulator": "6.193977757394317331203224447330934756768386116",
  "points": [
    [
      "90",
      "-532"
    ],
    [
      "64",
      "-170"
    ],
    [
      "526/9",
      "-2960/27"
    ],
    [
      "79",
      "-370"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1588 via the rational 2-torsion point x=211. 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 20:21:30",
  "updated_at": "2026-09-26 20:21:30"
}