{
  "id": 2716,
  "curve_key": "5753369585296:-13772377633490622656",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-119861866360",
    "15940291844569600"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    4,
    2
  ],
  "naive_height": 88.14242044179676,
  "faltings_height": 5.144815750803962,
  "conductor": "676608240",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "19",
    "41",
    "47"
  ],
  "discriminant": "442943263104900399961486899840000",
  "regulator": "23.512514479752678090499761159735719648407312",
  "points": [
    [
      "211132",
      "-6718932"
    ],
    [
      "1919020/9",
      "-236838140/27"
    ],
    [
      "3438601/16",
      "-661028445/64"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1569 via the rational 2-torsion point x=-385039. 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 20:19:02",
  "updated_at": "2026-09-26 20:19:02"
}