{"rank":3,"n":11,"seq":282747,"label":"3.11.282747","id":"r3_n11_00000000000****0****0****0****000000****0****00***00***00****0******00***00*0****0**0****0********0****00**00***00******0****0********0****00**00***00******000000000","beta_invariant":3,"birational_type":"empty","birational_type_components":"[]","birational_type_method":"empty_char0","char_poly_splits":true,"char_set":"[0]","expected_dimension_over_Z":0,"free_realization_space":false,"girth":2,"good_basis":null,"good_basis_v2":"1,3,8","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":null,"is_transversal":false,"is_uniform":null,"n_automorphisms":384,"n_bases":104,"n_circuits":69,"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":true,"rs_is_smooth_over_QQ":null,"rs_is_smooth_over_ZZ":false,"rs_n_qbar_components":null,"rs_regularity_method":"simple_core","rs_regularity_witness":"r3_n7_0******0******0***0******0*0**0****","rs_scheme_simple_core_id":"r3_n7_0******0******0***0******0*0**0****","rs_singular_fiber_characteristics":null,"rs_singular_fiber_characteristics_method":null,"rs_singular_fiber_primes":"[]","rs_singular_fiber_primes_method":"simple_core","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 + 4*x_0^2*x_1 + 4*x_0^2 + 6*x_0*x_1^3 + 12*x_0*x_1^2 + 11*x_0*x_1 + 3*x_0 + x_1^8 + 3*x_1^7 + 6*x_1^6 + 10*x_1^5 + 15*x_1^4 + 15*x_1^3 + 10*x_1^2 + 3*x_1","realization_space":{"vars":[],"ideal":["2"],"inequations":[],"matrix":[["1","1","0","0","1","1","1","0","1","0","0"],["0","0","1","1","1","0","0","0","1","1","1"],["0","0","0","0","0","1","1","1","1","1","1"]]}}