{
  "id": 2560,
  "curve_key": "293521:20641319",
  "ainvs": [
    "1",
    "0",
    "0",
    "-6115",
    "-24400"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    2,
    2
  ],
  "naive_height": 37.76911339783868,
  "faltings_height": 1.214635037094115,
  "conductor": "1785",
  "bad_primes": [
    "3",
    "5",
    "7",
    "17"
  ],
  "discriminant": "14387797265625",
  "regulator": "0.5059128678127379779529255244855486179114",
  "points": [
    [
      "455",
      "-9790"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#2077 via the rational 2-torsion point x=38. 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 20:09:13",
  "updated_at": "2026-09-26 20:09:13"
}