{
  "id": 2720,
  "curve_key": "4819008:-10095321600",
  "ainvs": [
    "0",
    "0",
    "0",
    "-100396",
    "11684400"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    2,
    2
  ],
  "naive_height": 46.164235967149644,
  "faltings_height": 1.7821282224478672,
  "conductor": "279616",
  "bad_primes": [
    "2",
    "17",
    "257"
  ],
  "discriminant": "5784446990024704",
  "regulator": "20.637741636575293647898939040224462110855782",
  "points": [
    [
      "4801/16",
      "-187425/64"
    ],
    [
      "857/4",
      "-771/8"
    ],
    [
      "664",
      "-15420"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1523 via the rational 2-torsion point x=-300. 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 20:19:13",
  "updated_at": "2026-09-26 20:19:13"
}