{"rank":3,"n":12,"seq":2072536,"label":"3.12.2072536","id":"r3_n12_0******0******0**********0********0*******0****0******************0********************************0**************0*****************************0*******0****0******************************************0***0*****0*********","beta_invariant":29,"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":3,"good_basis":null,"good_basis_v2":"1,4,8","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":true,"is_paving":true,"is_quaternary":false,"is_realizable":true,"is_realizable_char0":true,"is_regular":false,"is_self_dual":false,"is_series_parallel":false,"is_simple":true,"is_simplicial_arrangement":false,"is_supersolvable":false,"is_ternary":false,"is_three_lines":true,"is_transversal":false,"is_uniform":null,"kodaira_dimension":null,"kodaira_dimension_components":null,"kodaira_dimension_method":null,"n_automorphisms":1,"n_bases":204,"n_circuits":367,"n_components":null,"n_connected_components":1,"n_cyclic_flats":18,"n_flats":48,"n_loops":0,"principal_ideal":false,"rs_characteristic_dimension_unexpected":false,"rs_characteristic_dimension_varies":false,"rs_characteristic_dimensions":"[{\"p\":0,\"d\":0}]","rs_characteristic_dimensions_method":"exact_flatness_and_exceptional_fibers","rs_dim":7,"rs_is_regular_scheme":null,"rs_is_smooth_over_QQ":true,"rs_is_smooth_over_ZZ":false,"rs_n_q_components":1,"rs_n_qbar_components":3,"rs_regularity_method":null,"rs_regularity_witness":null,"rs_scheme_simple_core_id":null,"rs_singular_fiber_characteristics":"{\"kind\":\"finite\",\"primes\":[\"19\"]}","rs_singular_fiber_characteristics_method":"reused_direct_equidimensional_jacobian_certificate","rs_singular_fiber_primes":null,"rs_singular_fiber_primes_method":null,"rs_smoothness_method":"direct_equidimensional_jacobian_certificate","rs_smoothness_witness":"19","singular_primes":null,"smooth_char_0":null,"status":"computed_realization_space","tutte_polynomial":"x_0^3 + 9*x_0^2 + 16*x_0*x_1 + 29*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 + 36*x_1^2 + 29*x_1","realization_space":{"vars":["x1","x2"],"ideal":["13*x1 + 3*x2^2 - 7*x2 - 1","2*x1*x2 + 3*x1 + x2^2 - 5*x2","2*x1^2 + x1 + x2^2 - 2*x2","x1*x2 + 8*x1 + x2^3 - x2^2 + x2 - 1","x1^2 + x1*x2^2 + x1*x2 + 3*x1 - 5*x2"],"inequations":["x2 - 1","3*x1 + x2^2 - x2","3*x1^2 + x1*x2^2 + 2*x1*x2 - 6*x1 + x2^3 - 5*x2^2 + 5*x2 - 1","7*x1 + 2*x2^2 - 5*x2 + 1","3*x1^2 + x1*x2^2 + 2*x1*x2 - 3*x1 + x2^3 - 4*x2^2 + 2*x2","12*x1^2 + 7*x1*x2^2 - 7*x1*x2 - 3*x1 + x2^4 - 2*x2^3 - 2*x2^2 + 4*x2 - 1","3*x1 + x2^2 - 2*x2 + 1","3*x1*x2 + x1 + x2^3 - 2*x2^2 + x2 - 1","3*x1^2 + x1*x2^2 - 5*x1*x2 - 3*x1 - x2^3 + x2^2 + x2","20*x1^2 + 9*x1*x2^2 - 27*x1*x2 - 7*x1 + x2^4 - 6*x2^3 + 7*x2^2 + 4*x2","20*x1^2 + 9*x1*x2^2 - 27*x1*x2 - 4*x1 + x2^4 - 6*x2^3 + 8*x2^2 + 2*x2 + 1","55*x1^2 + 26*x1*x2^2 - 73*x1*x2 - 9*x1 + 3*x2^4 - 17*x2^3 + 21*x2^2 + 6*x2 - 1","20*x1^2 + 9*x1*x2^2 - 27*x1*x2 - 7*x1 + x2^4 - 6*x2^3 + 7*x2^2 + 5*x2 - 1","35*x1^2 + 17*x1*x2^2 - 46*x1*x2 - 5*x1 + 2*x2^4 - 11*x2^3 + 13*x2^2 + 4*x2 - 2","35*x1^2 + 17*x1*x2^2 - 38*x1*x2 - 7*x1 + 2*x2^4 - 9*x2^3 + 8*x2^2 + 5*x2","35*x1^2 + 17*x1*x2^2 - 38*x1*x2 - 10*x1 + 2*x2^4 - 9*x2^3 + 7*x2^2 + 7*x2 - 1","20*x1^2 + 9*x1*x2^2 - 19*x1*x2 - 12*x1 + x2^4 - 4*x2^3 + x2^2 + 8*x2","79*x1^2 + 40*x1*x2^2 - 96*x1*x2 - 6*x1 + 5*x2^4 - 24*x2^3 + 27*x2^2 + 5*x2 - 1","7*x1 + 2*x2^2 - 5*x2","4*x1 + x2^2 - 3*x2","11*x1 + 3*x2^2 - 8*x2 + 1","21*x1^2 + 13*x1*x2^2 - 33*x1*x2 + 14*x1 + 2*x2^4 - 10*x2^3 + 17*x2^2 - 10*x2 + 1","21*x1^2 + 13*x1*x2^2 - 33*x1*x2 + 3*x1 + 2*x2^4 - 10*x2^3 + 14*x2^2 - 2*x2","12*x1^2 + 7*x1*x2^2 - 24*x1*x2 + 11*x1 + x2^4 - 7*x2^3 + 14*x2^2 - 9*x2 + 1","3*x1*x2 - 7*x1 + x2^3 - 4*x2^2 + 5*x2","3*x1*x2 - 7*x1 + x2^3 - 4*x2^2 + 6*x2 - 1","21*x1^2 + 13*x1*x2^2 - 26*x1*x2 + 3*x1 + 2*x2^4 - 8*x2^3 + 9*x2^2 - x2","7*x1 + 2*x2^2 - 4*x2","23*x1^2 + 10*x1*x2^2 - 25*x1*x2 + x1 + x2^4 - 5*x2^3 + 6*x2^2 + x2 - 1","23*x1^2 + 10*x1*x2^2 - 25*x1*x2 - 10*x1 + x2^4 - 5*x2^3 + 3*x2^2 + 8*x2 - 1","47*x1^2 + 24*x1*x2^2 - 53*x1*x2 - 5*x1 + 3*x2^4 - 13*x2^3 + 12*x2^2 + 6*x2 - 2","4*x1 + x2^2 - 2*x2 - 1","4*x1 + x2^2 - 3*x2 + 1","9*x1^2 + 6*x1*x2^2 - 12*x1*x2 - 4*x1 + x2^4 - 4*x2^3 + 3*x2^2 + 3*x2 - 1"],"matrix":[["1","1","1","0","1","1","1","0","1","1","0","1"],["0","1","-3*x1 - x2^2 + 2*x2","1","1","-3*x1 - x2^2 + 2*x2","4*x1 + x2^2 - 3*x2 + 1","0","x1","-7*x1 - 2*x2^2 + 5*x2","1","x1"],["0","1","-3*x1 - x2^2 + 2*x2","0","0","1","-3*x1 - x2^2 + 2*x2","1","5*x1 + x2^2 - 2*x2 - 1","x2","-5*x1 - x2^2 + 3*x2 + 1","x2"]]}}