{
  "id": 2519,
  "curve_key": "625:-11753",
  "ainvs": [
    "1",
    "1",
    "1",
    "-13",
    "8"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    2
  ],
  "naive_height": 19.313254949209206,
  "faltings_height": -0.37136468463084144,
  "conductor": "429",
  "bad_primes": [
    "3",
    "11",
    "13"
  ],
  "discriminant": "61347",
  "regulator": "0.3490100016151185881828583574632160070796",
  "points": [
    [
      "-2",
      "6"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1798 via the rational 2-torsion point x=-1. 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 20:06:39",
  "updated_at": "2026-09-26 20:06:39"
}