{"rank":4,"n":9,"seq":158263,"label":"4.9.158263","id":"r4_n9_000000*********0************0******0*************0***********0********0************************0********0*******0****0********","beta_invariant":21,"birational_type":"K3 surface","birational_type_components":"[{\"dim\":2,\"free_rank\":0,\"torus_rank\":0,\"core_dim\":2,\"qbar_components\":1,\"type\":\"K3 surface\",\"elliptic_fibration\":{\"chi\":2,\"over\":\"x2\",\"singular_fibres\":[\"I1*\",\"I1*\",\"I1 (deg 2 place)\",\"I8\"],\"euler_number\":24,\"euler_check\":true,\"shioda_tate_lower_bound_rho\":19,\"j_constant\":false},\"core_vars\":[\"x2\",\"x3\",\"x4\"],\"core_gens\":[\"x2^2*x3*x4^2 - x2^2*x3*x4 - x2*x3^2*x4 - x2*x3*x4^2 + x2*x3^2 + 3*x2*x3*x4 - x2*x3 - x3^2 - x2*x4 + x3\"],\"n_linear_eliminations\":1}]","birational_type_method":"surface_elliptic_fibration_chi","char_poly_splits":false,"char_set":"[]","expected_dimension_over_Z":null,"free_realization_space":false,"girth":3,"good_basis":null,"good_basis_v2":"1,2,4,6","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":true,"is_paving":false,"is_quaternary":false,"is_realizable":false,"is_realizable_char0":false,"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":null,"is_transversal":false,"is_uniform":null,"n_automorphisms":1,"n_bases":110,"n_circuits":75,"n_components":null,"n_connected_components":1,"n_cyclic_flats":11,"n_flats":91,"n_loops":0,"principal_ideal":false,"rs_characteristic_dimension_unexpected":null,"rs_characteristic_dimension_varies":null,"rs_characteristic_dimensions":null,"rs_characteristic_dimensions_method":null,"rs_dim":-1,"rs_is_regular_scheme":null,"rs_is_smooth_over_QQ":null,"rs_is_smooth_over_ZZ":null,"rs_n_qbar_components":null,"rs_regularity_method":null,"rs_regularity_witness":null,"rs_scheme_simple_core_id":null,"rs_singular_fiber_characteristics":null,"rs_singular_fiber_characteristics_method":null,"rs_singular_fiber_primes":null,"rs_singular_fiber_primes_method":null,"rs_smoothness_method":null,"rs_smoothness_witness":null,"singular_primes":"[7]","smooth_char_0":true,"status":"computed_realization_space","tutte_polynomial":"x_0^4 + 5*x_0^3 + x_0^2*x_1 + 14*x_0^2 + x_0*x_1^2 + 12*x_0*x_1 + 21*x_0 + x_1^5 + 4*x_1^4 + 10*x_1^3 + 19*x_1^2 + 21*x_1","realization_space":{"vars":["x1","x2","x3","x4"],"ideal":["x1*x2 - x1*x3 + x2*x4 - x2 - x4 + 1","x1*x3^2*x4 - x1*x3^2 + x1*x3 - x2*x3*x4^2 + x2*x3*x4 + x3*x4^2 - 2*x3*x4 + x4","x2^2*x3*x4^2 - x2^2*x3*x4 - x2*x3^2*x4 + x2*x3^2 - x2*x3*x4^2 + 3*x2*x3*x4 - x2*x3 - x2*x4 - x3^2 + x3"],"inequations":["x2*x3*x4 - x2*x4^2 - x3^2 + x3","x2*x4 - x3 - x4 + 1","x3","x2*x4 - x3","x4 - 1","x1*x3 - x3 + x4","x3 - x4","x4","x2","x2 - x3","x1*x2*x4 - x1*x3 - x4 + 1","x1 - 1","x1*x3 + x4 - 1","x3 - 1","x1 + x4 - 1","x1","x1*x3 - x2*x4 + x4","x1*x2*x3*x4 - x1*x3^2 + x1*x3 - x2*x3*x4 + x3^2 - x3 + x4","x1*x3 - x3 + 1","x2*x4 - x3 + 1","x1*x3 + x4","x2 - 1","x1*x2 - x2 + 1"],"matrix":[["1","0","1","0","1","0","1","0","1"],["0","1","1","0","x1","0","0","x3*x4 - x4","-x4 + 1"],["0","0","0","1","1","0","x2","-x3^2 + x3","x3"],["0","0","0","0","0","1","1","-x3*x4","x4"]]}}