{
  "id": 2700,
  "curve_key": "27217953:-130364170065",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-567041",
    "151026216"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    2,
    2
  ],
  "naive_height": 51.3581620509074,
  "faltings_height": 2.2436982466915487,
  "conductor": "503217",
  "bad_primes": [
    "3",
    "11",
    "13",
    "17",
    "23"
  ],
  "discriminant": "1833741037108360809",
  "regulator": "3.2363244699029097013327712527529821360470308",
  "points": [
    [
      "-19851/49",
      "6148575/343"
    ],
    [
      "15821/16",
      "-1541325/64"
    ],
    [
      "2054",
      "-88485"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1526 via the rational 2-torsion point x=431. 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 20:18:21",
  "updated_at": "2026-09-26 20:18:21"
}