{
  "pair_factor": {
    "ring": "R = Z_3[eta]/(eta^2 - 3 eta)",
    "fiber_product_model": "R \u2245 Z_3 \u00d7_{F_3} Z_3",
    "normalization": "S = Z_3 \u00d7 Z_3",
    "conductor": "f = 3S = m",
    "maximal_ideal": "m = (3,eta)",
    "krull_dimension": 1,
    "embedding_dimension": 2,
    "complete_intersection": true,
    "gorenstein": true,
    "overorders": [
      "R",
      "S"
    ]
  },
  "associated_graded": {
    "gr_m_R": "F_3[a,g]/(g^2 - a g)",
    "degree_1_generators": {
      "a": "class of 3 in m/m^2",
      "g": "class of eta in m/m^2"
    },
    "tangent_cone": "Spec(F_3[a,g]/(g(g-a)))",
    "hilbert_series_pair": "(1+t)/(1-t)",
    "hilbert_series_singular_order": "(2+t)/(1-t)"
  },
  "ideal_count_by_index_pair_factor": {
    "c_0": 1,
    "c_odd_2r_minus_1": 1,
    "c_even_2r": 4,
    "local_ideal_zeta": "(1 + x + 3 x^2)/(1 - x^2)",
    "variable": "x = 3^{-s}"
  },
  "ideal_count_by_index_full_singular_order": {
    "local_ideal_zeta": "(1 + x + 3 x^2)/((1 - x)(1 - x^2))",
    "variable": "x = 3^{-s}"
  }
}