{
  "id": 2870,
  "curve_key": "1083670416:17650193820480",
  "ainvs": [
    "0",
    "0",
    "0",
    "-22576467",
    "-20428465070"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2
  ],
  "naive_height": 62.41085894835777,
  "faltings_height": 3.252274247565778,
  "conductor": "138417695568",
  "bad_primes": [
    "2",
    "3",
    "19",
    "43",
    "71",
    "73",
    "227"
  ],
  "discriminant": "556174696958373851615232",
  "regulator": "244.70918997284217677420076965011915140599988490238",
  "points": [
    [
      "-961",
      "-19494"
    ],
    [
      "17849",
      "-2294136"
    ],
    [
      "388919",
      "-242524854"
    ],
    [
      "6194",
      "-278154"
    ],
    [
      "-4191",
      "-24016"
    ],
    [
      "-76999/25",
      "-17628624/125"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1297 via the rational 2-torsion point x=2105. 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 20:26:11",
  "updated_at": "2026-09-26 20:26:11"
}