{"rank":3,"n":12,"seq":28797771,"label":"3.12.28797771","id":"r3_n12_00000****00****000**0****0**00*****0****0******00*******0****0*********00********0**0****0**************0****0******0**00****0***************00**********0****00*****0****0*********************0**00****00***********0*****","beta_invariant":13,"birational_type":null,"birational_type_components":null,"birational_type_method":null,"char_poly_splits":false,"char_set":"[0]","expected_dimension_over_Z":-1,"free_realization_space":false,"girth":2,"good_basis":null,"good_basis_v2":"3,5,8","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":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":false,"is_ternary":false,"is_three_lines":false,"is_transversal":false,"is_uniform":null,"n_automorphisms":32,"n_bases":176,"n_circuits":235,"n_components":null,"n_connected_components":1,"n_cyclic_flats":18,"n_flats":28,"n_loops":0,"principal_ideal":false,"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":4,"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_n10_0000************0**********0****0**********0****0****************0*****0******0****************0******0**0********0*****","singular_primes":null,"smooth_char_0":null,"status":"computed_realization_space","tutte_polynomial":"x_0^3 + 2*x_0^2*x_1 + 7*x_0^2 + 10*x_0*x_1^2 + 20*x_0*x_1 + 13*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 + 28*x_1^3 + 26*x_1^2 + 13*x_1","realization_space":{"vars":["x1"],"ideal":["2","x1^2 + x1 + 1"],"inequations":[],"matrix":[["1","1","0","0","1","0","1","0","1","1","1","1"],["x1","x1","0","0","0","1","0","1","1","-x1 + 1","-x1 + 1","1"],["1","1","1","1","0","-x1 + 1","x1","0","0","0","1","x1"]]}}