{
  "id": 2745,
  "curve_key": "2575734782608:1206651051550220480",
  "ainvs": [
    "0",
    "1",
    "0",
    "-53661141304",
    "-1396604752267264"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    2,
    2
  ],
  "naive_height": 85.73146788542431,
  "faltings_height": 5.20713833714832,
  "conductor": "2428381032",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "19",
    "23",
    "31",
    "97"
  ],
  "discriminant": "9046570017216325919628185846498304",
  "regulator": "219.0215881641677935327224328992763001102466828",
  "points": [
    [
      "-66793",
      "43469580"
    ],
    [
      "14476019/25",
      "-50261391378/125"
    ],
    [
      "8278784/25",
      "-16368800448/125"
    ],
    [
      "2595589/4",
      "-3894717519/8"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#2122 via the rational 2-torsion point x=108668. 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 20:20:25",
  "updated_at": "2026-09-26 20:20:25"
}