{
  "id": 2872,
  "curve_key": "-194957159:-760047144445",
  "ainvs": [
    "1",
    "0",
    "1",
    "4061607",
    "880022662"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2
  ],
  "naive_height": 57.26487118486532,
  "faltings_height": 2.8461850519469873,
  "conductor": "121340359518",
  "bad_primes": [
    "2",
    "3",
    "7",
    "43",
    "193",
    "337",
    "1033"
  ],
  "discriminant": "-4622488801102933909218",
  "regulator": "661.72064388366632428929385969753112102735312307552",
  "points": [
    [
      "-172",
      "13365"
    ],
    [
      "338",
      "47700"
    ],
    [
      "656",
      "61533"
    ],
    [
      "1346",
      "93060"
    ],
    [
      "10904/25",
      "-6563943/125"
    ],
    [
      "9980",
      "-1022562"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1235 via the rational 2-torsion point x=107. 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 20:26:14",
  "updated_at": "2026-09-26 20:26:14"
}