{
  "id": 2588,
  "curve_key": "-4719:-130329",
  "ainvs": [
    "1",
    "-1",
    "1",
    "98",
    "126"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    4
  ],
  "naive_height": 25.378056575179162,
  "faltings_height": 0.19480967309203645,
  "conductor": "205",
  "bad_primes": [
    "5",
    "41"
  ],
  "discriminant": "-70644025",
  "regulator": "1.602601397324700955066904509537931569839",
  "points": [
    [
      "1",
      "-16"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#2073 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 20:11:12",
  "updated_at": "2026-09-26 20:11:12"
}