{"rank":3,"n":12,"seq":31252949,"label":"3.12.31252949","id":"r3_n12_00000000000*********0*********00***0***********0*****0**0***********0******0***0**0*0***********0**********0**0***0**0*00************0***0*******0**00***************0*************0**0*************0****00*********0***0***","beta_invariant":15,"birational_type":null,"birational_type_components":null,"birational_type_method":null,"char_poly_splits":true,"char_set":"[0]","expected_dimension_over_Z":-1,"free_realization_space":false,"girth":2,"good_basis":null,"good_basis_v2":"3,4,9","is_binary":false,"is_coloopless":true,"is_connected":true,"is_divisionally_free":true,"is_graphic":false,"is_identically_self_dual":false,"is_laminar":false,"is_loopless":true,"is_nested":false,"is_orientable":false,"is_paving":false,"is_quaternary":false,"is_realizable":true,"is_realizable_char0":true,"is_regular":false,"is_self_dual":false,"is_series_parallel":false,"is_simple":false,"is_simplicial_arrangement":false,"is_supersolvable":true,"is_ternary":false,"is_three_lines":false,"is_transversal":false,"is_uniform":null,"n_automorphisms":4,"n_bases":177,"n_circuits":223,"n_components":null,"n_connected_components":1,"n_cyclic_flats":15,"n_flats":31,"n_loops":0,"principal_ideal":true,"rs_characteristic_dimension_unexpected":false,"rs_characteristic_dimension_varies":false,"rs_characteristic_dimensions":"[]","rs_characteristic_dimensions_method":"empty","rs_dim":4,"rs_is_regular_scheme":null,"rs_is_smooth_over_QQ":true,"rs_is_smooth_over_ZZ":true,"rs_n_qbar_components":null,"rs_regularity_method":null,"rs_regularity_witness":null,"rs_scheme_simple_core_id":null,"rs_singular_fiber_characteristics":"{\"kind\":\"finite\",\"primes\":[]}","rs_singular_fiber_characteristics_method":"smooth_over_ZZ","rs_singular_fiber_primes":null,"rs_singular_fiber_primes_method":null,"rs_smoothness_method":"empty","rs_smoothness_witness":null,"singular_primes":null,"smooth_char_0":null,"status":"computed_realization_space","tutte_polynomial":"x_0^3 + x_0^2*x_1 + 8*x_0^2 + 2*x_0*x_1^3 + 8*x_0*x_1^2 + 19*x_0*x_1 + 15*x_0 + x_1^9 + 3*x_1^8 + 6*x_1^7 + 10*x_1^6 + 15*x_1^5 + 21*x_1^4 + 26*x_1^3 + 26*x_1^2 + 15*x_1","realization_space":{"vars":["x1","x2","x3","x4","x5"],"ideal":["1"],"inequations":["0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"],"matrix":null}}