{
  "id": 2661,
  "curve_key": "27873:-3811185",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-581",
    "4556"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    2,
    2
  ],
  "naive_height": 30.706241271928267,
  "faltings_height": 0.5625048425322432,
  "conductor": "7137",
  "bad_primes": [
    "3",
    "13",
    "61"
  ],
  "discriminant": "4125878289",
  "regulator": "2.51917071157942541053315104805253347003352",
  "points": [
    [
      "-18",
      "103"
    ],
    [
      "48",
      "-317"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1430 via the rational 2-torsion point x=219/4. 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 20:16:24",
  "updated_at": "2026-09-26 20:16:24"
}