{
  "id": 2583,
  "curve_key": "-486433919:-367535114641729",
  "ainvs": [
    "1",
    "0",
    "0",
    "10134040",
    "425388708672"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    8
  ],
  "naive_height": 67.07567996012469,
  "faltings_height": 3.6475266189092226,
  "conductor": "82110",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "17",
    "23"
  ],
  "discriminant": "-78239096930039062500000000",
  "regulator": "4.069730484363187393043275250556656602285",
  "points": [
    [
      "-44744/9",
      "13624616/27"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1073 via the rational 2-torsion point x=3536. Independent witness points are the images of that curve's witnesses under the degree-2 isogeny.",
  "created_at": "2026-09-26 20:10:53",
  "updated_at": "2026-09-26 20:10:53"
}