{
  "id": 1748,
  "curve_key": "15313921:-64520225281",
  "ainvs": [
    "1",
    "0",
    "0",
    "-319040",
    "74649600"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    7
  ],
  "naive_height": 49.78048916368665,
  "faltings_height": 2.1042660141403324,
  "conductor": "27690",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "71"
  ],
  "discriminant": "-330727587840000000",
  "regulator": "1.751933353676479625160961243000059873368",
  "points": [
    [
      "-620",
      "6160"
    ]
  ],
  "submitter": "hdeping",
  "history": [],
  "commentary": "Specialization t=-5/3 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 10:47:35",
  "updated_at": "2026-09-25 10:47:35"
}