{"rank":3,"n":11,"seq":282599,"label":"3.11.282599","id":"r3_n11_00000000000****0****0****0****000000****0****00***00***00****0********0****00*******0****0**************0**00***00******0****0**************0****0****00*********00**","beta_invariant":7,"birational_type":"point over Q(a)/(a^2 - a + 1)","birational_type_components":"[{\"dim\":0,\"free_rank\":0,\"torus_rank\":0,\"core_dim\":0,\"qbar_components\":2,\"type\":\"point over Q(a)/(a^2 - a + 1)\",\"field\":\"Q(a)/(a^2 - a + 1)\",\"minpoly\":\"T^2 - T + 1\",\"degree\":2,\"core_vars\":[\"x1\"],\"core_gens\":[\"x1^2 - x1 + 1\"]}]","birational_type_method":"point_field","char_poly_splits":false,"char_set":"[0]","expected_dimension_over_Z":1,"free_realization_space":false,"girth":2,"good_basis":null,"good_basis_v2":"1,3,6","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":true,"is_three_lines":null,"is_transversal":false,"is_uniform":null,"n_automorphisms":16,"n_bases":119,"n_circuits":121,"n_components":null,"n_connected_components":1,"n_cyclic_flats":14,"n_flats":22,"n_loops":0,"principal_ideal":true,"rs_characteristic_dimension_unexpected":false,"rs_characteristic_dimension_varies":false,"rs_characteristic_dimensions":"[{\"p\":0,\"d\":0}]","rs_characteristic_dimensions_method":"simple_core","rs_dim":4,"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_n8_0******0******0**********0********0*******0****0**0*****","rs_scheme_simple_core_id":"r3_n8_0******0******0**********0********0*******0****0**0*****","rs_singular_fiber_characteristics":null,"rs_singular_fiber_characteristics_method":null,"rs_singular_fiber_primes":"[3]","rs_singular_fiber_primes_method":"simple_core","rs_smoothness_method":"simple_core","rs_smoothness_witness":"r3_n8_0******0******0**********0********0*******0****0**0*****","singular_primes":null,"smooth_char_0":null,"status":"computed_realization_space","tutte_polynomial":"x_0^3 + 3*x_0^2*x_1 + 5*x_0^2 + 2*x_0*x_1^3 + 10*x_0*x_1^2 + 14*x_0*x_1 + 7*x_0 + x_1^8 + 3*x_1^7 + 6*x_1^6 + 10*x_1^5 + 15*x_1^4 + 19*x_1^3 + 16*x_1^2 + 7*x_1","realization_space":{"vars":["x1"],"ideal":["x1^2 - x1 + 1"],"inequations":[],"matrix":[["1","1","0","0","1","0","0","1","1","1","1"],["0","0","1","1","1","0","0","0","1","-x1 + 1","-x1 + 1"],["0","0","0","0","0","1","1","1","x1","1","x1"]]}}