{
  "id": 1769,
  "curve_key": "267948561:-4386156984441",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-5582262",
    "5077966149"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    7
  ],
  "naive_height": 58.218949114899864,
  "faltings_height": 2.4932317077383535,
  "conductor": "4730",
  "bad_primes": [
    "2",
    "5",
    "11",
    "43"
  ],
  "discriminant": "-360317791790000000",
  "regulator": "0.9820573051492007438543485896172307604395",
  "points": [
    [
      "-2493",
      "60371"
    ]
  ],
  "submitter": "hdeping",
  "history": [],
  "commentary": "Specialization t=-10/1 of the universal X_1(7) Tate normal form family y^2+(-t^2+t+1)xy+(-t^3+t^2)y=x^3+(-t^3+t^2)x^2 (K3 elliptic surface, rational 7-torsion point (0,0)).",
  "created_at": "2026-09-25 14:22:01",
  "updated_at": "2026-09-25 14:22:01"
}