{
  "id": 2586,
  "curve_key": "553:12779",
  "ainvs": [
    "1",
    "0",
    "1",
    "-12",
    "-16"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    2
  ],
  "naive_height": 18.946074004567006,
  "faltings_height": -0.5315800108842762,
  "conductor": "82",
  "bad_primes": [
    "2",
    "41"
  ],
  "discriminant": "3362",
  "regulator": "0.4494138498377561644575907202691624852156",
  "points": [
    [
      "-2",
      "1"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1794 via the rational 2-torsion point x=1. Independent witness points are the images of that curve's witnesses under the degree-2 isogeny.",
  "created_at": "2026-09-26 20:11:04",
  "updated_at": "2026-09-26 20:11:04"
}