{"rank":3,"n":12,"seq":31849895,"label":"3.12.31849895","id":"r3_n12_00000000000000000000000******0*****000******0*****000000000******0*****000***000***0000******0********00****00*0*****0**000******0********00****00*0*****0**000000000000******0**********0*****00***00***000******000******0","beta_invariant":3,"birational_type":null,"birational_type_components":null,"birational_type_method":null,"char_poly_splits":true,"char_set":"[0]","expected_dimension_over_Z":0,"free_realization_space":false,"girth":2,"good_basis":null,"good_basis_v2":"1,4,7","is_binary":true,"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":true,"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":288,"n_bases":130,"n_circuits":89,"n_components":null,"n_connected_components":1,"n_cyclic_flats":13,"n_flats":16,"n_loops":0,"principal_ideal":true,"rs_characteristic_dimension_unexpected":true,"rs_characteristic_dimension_varies":false,"rs_characteristic_dimensions":"[{\"p\":2,\"d\":0}]","rs_characteristic_dimensions_method":"simple_core","rs_dim":1,"rs_is_regular_scheme":null,"rs_is_smooth_over_QQ":true,"rs_is_smooth_over_ZZ":false,"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":"complete_simple_core","rs_singular_fiber_primes":null,"rs_singular_fiber_primes_method":null,"rs_smoothness_method":"simple_core","rs_smoothness_witness":"r3_n7_0******0******0***0******0*0**0****","singular_primes":null,"smooth_char_0":null,"status":"computed_realization_space","tutte_polynomial":"x_0^3 + x_0^2*x_1^2 + 4*x_0^2*x_1 + 4*x_0^2 + 4*x_0*x_1^4 + 8*x_0*x_1^3 + 13*x_0*x_1^2 + 11*x_0*x_1 + 3*x_0 + x_1^9 + 3*x_1^8 + 6*x_1^7 + 10*x_1^6 + 15*x_1^5 + 17*x_1^4 + 16*x_1^3 + 10*x_1^2 + 3*x_1","realization_space":{"vars":[],"ideal":["2"],"inequations":[],"matrix":[["1","1","1","0","0","1","0","0","1","0","0","1"],["0","0","0","1","1","1","0","0","0","1","1","1"],["0","0","0","0","0","0","1","1","1","1","1","1"]]}}