{
  "id": 2765,
  "curve_key": "4243403035249:-8740346432912176393",
  "ainvs": [
    "1",
    "0",
    "0",
    "-88404229901",
    "10116134337740305"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    6
  ],
  "naive_height": 87.22915999773662,
  "faltings_height": 4.964261593123408,
  "conductor": "3913593970",
  "bad_primes": [
    "2",
    "5",
    "11",
    "13",
    "17",
    "19",
    "37",
    "229"
  ],
  "discriminant": "8709952210706687914927679897600",
  "regulator": "34.69979523882825681242709603816565344810298874",
  "points": [
    [
      "559314",
      "-368575585"
    ],
    [
      "827998",
      "-710749989"
    ],
    [
      "-307772",
      "90548751"
    ],
    [
      "-343302",
      "2456791"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1611 via the rational 2-torsion point x=-86526. 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 20:21:27",
  "updated_at": "2026-09-26 20:21:27"
}