{"rank":4,"n":9,"seq":102227,"label":"4.9.102227","id":"r4_n9_0********0****0*****0**0*****************0****0*********************0************************0**********0****************0****","beta_invariant":24,"birational_type":"rational over Q(a)/(a^2 + 1)","birational_type_components":"[{\"dim\":1,\"free_rank\":1,\"torus_rank\":1,\"core_dim\":0,\"qbar_components\":2,\"type\":\"rational over Q(a)/(a^2 + 1)\",\"field\":\"Q(a)/(a^2 + 1)\",\"minpoly\":\"T^2 + 1\",\"degree\":2,\"reason\":\"A^1 over the field of definition\",\"core_vars\":[\"x1\"],\"core_gens\":[\"x1^2 - 2*x1 + 2\"]}]","birational_type_method":"point_field","char_poly_splits":false,"char_set":"[0]","expected_dimension_over_Z":null,"free_realization_space":false,"girth":4,"good_basis":null,"good_basis_v2":"4,5,6,7","is_binary":false,"is_coloopless":true,"is_connected":true,"is_divisionally_free":false,"is_graphic":false,"is_identically_self_dual":false,"is_laminar":false,"is_loopless":true,"is_nested":false,"is_orientable":false,"is_paving":true,"is_quaternary":false,"is_realizable":true,"is_realizable_char0":true,"is_regular":false,"is_self_dual":false,"is_series_parallel":false,"is_simple":true,"is_simplicial_arrangement":false,"is_supersolvable":false,"is_ternary":false,"is_three_lines":null,"is_transversal":false,"is_uniform":null,"n_automorphisms":1,"n_bases":115,"n_circuits":82,"n_components":null,"n_connected_components":1,"n_cyclic_flats":13,"n_flats":98,"n_loops":0,"principal_ideal":true,"rs_characteristic_dimension_unexpected":null,"rs_characteristic_dimension_varies":null,"rs_characteristic_dimensions":null,"rs_characteristic_dimensions_method":null,"rs_dim":4,"rs_is_regular_scheme":null,"rs_is_smooth_over_QQ":null,"rs_is_smooth_over_ZZ":null,"rs_n_qbar_components":null,"rs_regularity_method":null,"rs_regularity_witness":null,"rs_scheme_simple_core_id":null,"rs_singular_fiber_characteristics":null,"rs_singular_fiber_characteristics_method":null,"rs_singular_fiber_primes":null,"rs_singular_fiber_primes_method":null,"rs_smoothness_method":null,"rs_smoothness_witness":null,"singular_primes":"[]","smooth_char_0":true,"status":"computed_realization_space","tutte_polynomial":"x_0^4 + 5*x_0^3 + 15*x_0^2 + 11*x_0*x_1 + 24*x_0 + x_1^5 + 4*x_1^4 + 10*x_1^3 + 20*x_1^2 + 24*x_1","realization_space":{"vars":["x1","x2"],"ideal":["x1^2 - 2*x1 + 2"],"inequations":["2","x1 + x2 - 1","x2 + 1","x1*x2 - x1 - 2*x2","x1","x2","x1*x2 + x1 - 1","x1*x2 + x1 - x2","x2 - 1","x1*x2 + x1 - 2*x2","x1*x2 + x1 - 2","x1*x2 - x2 - 1","x1 - 2","2*x1*x2 - 3*x2 - 1","2*x1 - 1","2*x1 - 3"],"matrix":[["1","1","1","1","0","0","0","1","0"],["1","x1 - 1","-x1 + 2","0","1","0","0","0","1"],["1","0","1","0","0","1","0","-x1 + 1","1"],["1","1","0","0","0","0","1","x1","x2"]]}}