{
  "id": 1749,
  "curve_key": "21613089:-100490410161",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-450273",
    "116420913"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    7
  ],
  "naive_height": 50.66665627721812,
  "faltings_height": 1.921877153707782,
  "conductor": "10766",
  "bad_primes": [
    "2",
    "7",
    "769"
  ],
  "discriminant": "-1328135939293184",
  "regulator": "3.091150269156805906062455600585450367700",
  "points": [
    [
      "-177",
      "13892"
    ]
  ],
  "submitter": "hdeping",
  "history": [],
  "commentary": "Specialization t=-7/1 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 10:47:42",
  "updated_at": "2026-09-25 10:47:42"
}