{
  "id": 2687,
  "curve_key": "556608:-404974080",
  "ainvs": [
    "0",
    "0",
    "0",
    "-11596",
    "468720"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    2,
    2
  ],
  "naive_height": 39.68884950284831,
  "faltings_height": 1.2134177550138125,
  "conductor": "552512",
  "bad_primes": [
    "2",
    "89",
    "97"
  ],
  "discriminant": "4884312162304",
  "regulator": "27.247452235633422920741089602445361780519018",
  "points": [
    [
      "4582/49",
      "-154176/343"
    ],
    [
      "232",
      "-3204"
    ],
    [
      "14166/25",
      "-1657536/125"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1527 via the rational 2-torsion point x=-108. 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 20:17:45",
  "updated_at": "2026-09-26 20:17:45"
}