{
  "id": 2630,
  "curve_key": "635529553:8825514404615",
  "ainvs": [
    "1",
    "0",
    "0",
    "-13240199",
    "-10215819096"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    2,
    2
  ],
  "naive_height": 60.80990745315914,
  "faltings_height": 3.1140730634485227,
  "conductor": "503139",
  "bad_primes": [
    "3",
    "7",
    "13",
    "19",
    "97"
  ],
  "discriminant": "103471812430533743587209",
  "regulator": "3.85289129837949914417117622033012875475542",
  "points": [
    [
      "4717",
      "-182051"
    ],
    [
      "57610756/3025",
      "-430478092394/166375"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#2067 via the rational 2-torsion point x=1582. 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 20:13:51",
  "updated_at": "2026-09-26 20:13:51"
}