{
  "id": 2694,
  "curve_key": "502968608350273:-11271726544737952962145",
  "ainvs": [
    "1",
    "0",
    "0",
    "-10478512673964",
    "13045978923941019024"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    4,
    2
  ],
  "naive_height": 101.5546466257032,
  "faltings_height": 6.225366240782211,
  "conductor": "1242248154",
  "bad_primes": [
    "2",
    "3",
    "7",
    "73",
    "97",
    "4177"
  ],
  "discriminant": "108728054354148105879321146933670641664",
  "regulator": "68.137337013279127840793340406779038884814912",
  "points": [
    [
      "328684696/9",
      "-5936782872292/27"
    ],
    [
      "21581129592/10609",
      "-421637273266068/1092727"
    ],
    [
      "438486763320/229441",
      "-2344552489831572/109902239"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1564 via the rational 2-torsion point x=-14618305/4. 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 20:18:03",
  "updated_at": "2026-09-26 20:18:03"
}