{
  "id": 5577,
  "curve_key": "806051233:2518798348655",
  "ainvs": [
    "1",
    "0",
    "0",
    "-16792734",
    "-2916675261"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    4,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 61.522973588900676,
  "faltings_height": 3.1944148523288765,
  "conductor": "13086843",
  "bad_primes": [
    "3",
    "7",
    "11",
    "181",
    "313"
  ],
  "discriminant": "299399378257712257684929",
  "regulator": "99.291251080884117895108239840656829479082547",
  "points": [
    [
      "-3930",
      "50793"
    ],
    [
      "-11025/4",
      "1209189/8"
    ],
    [
      "-2286",
      "154527"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Specialization at (u,v) = (132,181) of the C2 x C4 family y^2 = x(x+u^2)(x+v^2), giving y^2 = x(x+17424)(x+32761). Found in my own run scanning coprime positive integer pairs u < v, with v <= 250. The displayed global minimal model [1,0,0,-16792734,-2916675261] is obtained by x = 4X - 16728, y = 8Y + 4X. Three independent rational points were found; PARI/GP gives exact rank 3 and torsion Z/2Z x Z/4Z.",
  "created_at": "2026-10-23 18:44:49",
  "updated_at": "2026-10-23 18:44:49"
}