{"rank":4,"n":7,"seq":60,"label":"4.7.60","id":"r4_n7_0000000000****000000****00****000**","beta_invariant":null,"birational_type":"rational","birational_type_components":"[{\"dim\":0,\"free_rank\":0,\"torus_rank\":0,\"core_dim\":0,\"qbar_components\":1,\"type\":\"rational\",\"reason\":\"rigid: unique realization over Q (integer matrix)\"}]","birational_type_method":"rigid","char_poly_splits":false,"char_set":"[0]","expected_dimension_over_Z":null,"free_realization_space":true,"girth":2,"good_basis":null,"good_basis_v2":"1,3,5,6","is_binary":true,"is_coloopless":true,"is_connected":false,"is_divisionally_free":false,"is_graphic":true,"is_identically_self_dual":null,"is_laminar":null,"is_loopless":true,"is_nested":null,"is_orientable":true,"is_paving":null,"is_quaternary":true,"is_realizable":true,"is_realizable_char0":true,"is_regular":true,"is_self_dual":null,"is_series_parallel":null,"is_simple":false,"is_simplicial_arrangement":false,"is_supersolvable":false,"is_ternary":true,"is_three_lines":null,"is_transversal":null,"is_uniform":false,"n_automorphisms":null,"n_bases":14,"n_circuits":4,"n_components":1,"n_connected_components":2,"n_cyclic_flats":null,"n_flats":24,"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":0,"rs_is_regular_scheme":null,"rs_is_smooth_over_QQ":null,"rs_is_smooth_over_ZZ":null,"rs_n_qbar_components":1,"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":null,"smooth_char_0":null,"status":"computed_realization_space","tutte_polynomial":"x^4 + 2*x^3*y + x^3 + x^2*y^2 + 2*x^2*y + x^2 + 2*x*y^2 + 2*x*y + y^3 + y^2","realization_space":{"vars":[],"ideal":["0"],"inequations":[],"matrix":[["1","1","0","0","0","0","1"],["0","0","1","1","0","0","0"],["0","0","0","0","1","0","1"],["0","0","0","0","0","1","1"]]}}