{"rank":3,"n":11,"seq":71890,"label":"3.11.71890","id":"r3_n11_0000************0**********0***************0***********************0***************0*****************0********0*****************************00**********************0","beta_invariant":23,"birational_type":"genus 1 curve (14a4) x P^1","birational_type_components":"[{\"dim\":2,\"free_rank\":1,\"torus_rank\":1,\"core_dim\":1,\"qbar_components\":1,\"type\":\"genus 1 curve x P^1\",\"genus\":1,\"cremona_label\":\"14a4\",\"conductor\":14,\"j_invariant\":\"-15625/28\",\"weierstrass\":\"[1, 0, 1, -1, 0]\",\"rank\":0,\"torsion_order\":6,\"core_vars\":[\"x2\",\"x3\"],\"core_gens\":[\"x2^2*x3 - x2*x3^2 + x2^2 - 3*x2*x3 + x3^2 + x3\"]}]","birational_type_method":"curve_genus+weierstrass_riemann_roch","char_poly_splits":false,"char_set":"[0]","expected_dimension_over_Z":3,"free_realization_space":false,"girth":3,"good_basis":"1,2,6","good_basis_v2":"1,3,7","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":false,"is_transversal":false,"is_uniform":null,"n_automorphisms":3,"n_bases":151,"n_circuits":235,"n_components":null,"n_connected_components":1,"n_cyclic_flats":13,"n_flats":43,"n_loops":0,"principal_ideal":true,"rs_characteristic_dimension_unexpected":false,"rs_characteristic_dimension_varies":false,"rs_characteristic_dimensions":"[{\"p\":0,\"d\":2}]","rs_characteristic_dimensions_method":"cofinite_strong_groebner_candidates_exact","rs_dim":4,"rs_is_regular_scheme":true,"rs_is_smooth_over_QQ":null,"rs_is_smooth_over_ZZ":true,"rs_n_qbar_components":null,"rs_regularity_method":"three_lines_deletion","rs_regularity_witness":"4=>r3_n10_0******0******0***0******0****************0***********************0****************0***************0*******0********0***","rs_scheme_simple_core_id":"r3_n11_0000************0**********0***************0***********************0***************0*****************0********0*****************************00**********************0","rs_singular_fiber_characteristics":null,"rs_singular_fiber_characteristics_method":null,"rs_singular_fiber_primes":"[]","rs_singular_fiber_primes_method":"smooth_over_ZZ","rs_smoothness_method":"three_lines_deletion","rs_smoothness_witness":"4=>r3_n10_0******0******0***0******0****************0***********************0****************0***************0*******0********0***","singular_primes":"[]","smooth_char_0":true,"status":"computed_realization_space","tutte_polynomial":"x_0^3 + 8*x_0^2 + x_0*x_1^2 + 12*x_0*x_1 + 23*x_0 + x_1^8 + 3*x_1^7 + 6*x_1^6 + 10*x_1^5 + 15*x_1^4 + 21*x_1^3 + 27*x_1^2 + 23*x_1","realization_space":{"vars":["x1","x2","x3"],"ideal":["x2^2*x3 + x2^2 - x2*x3^2 - 3*x2*x3 + x3^2 + x3"],"inequations":["x2^2*x3 + x2^2 - 2*x2*x3 - x3^3 + x3","x2^2*x3 + x2^2 - 3*x2*x3 - x2 - x3^3 + 3*x3","x2*x3 + x2 - 2*x3","x1*x2*x3 + x1*x2 - 2*x1*x3 - x2^2*x3 - x2^2 + 2*x2*x3 + x3^3 - x3","x2^2*x3 + x2^2 - 3*x2*x3 - x2 - x3^3 + x3^2 + 3*x3 - 1","x2 - x3","x3 - 1","x2","x2^2 - x2*x3 - x2 + 1","x2 - 1","x1*x2 - x1 - x2^2 + x2*x3","x2*x3 - 1","x1","x1 - x2","x1*x3 - x1 + x2 - x3","x3","x1 - 1","x2^2*x3 + x2^2 + x2*x3^3 - 3*x2*x3 - x3^4 - x3^3 + x3^2 + x3","x2^2*x3 + x2^2 + x2*x3^3 - x2*x3^2 - 4*x2*x3 - x3^4 - x3^3 + 3*x3^2 + x3","x1*x2*x3^2 + x1*x2*x3 - 2*x1*x3^2 - x2^2*x3 - x2^2 - x2*x3^3 + 3*x2*x3 + x3^4 + x3^3 - x3^2 - x3","x2*x3 + x2 + x3^3 - 3*x3","x2^2*x3 + x2^2 - 2*x2*x3^2 - 4*x2*x3 + x3^3 + 2*x3^2 + x3","x2^2*x3 + x2^2 - x2*x3^2 - 3*x2*x3 - x3^3 + 2*x3^2 + x3","x1*x2*x3^2 + x1*x2*x3 - 2*x1*x3^2 - x2^2*x3 - x2^2 + 2*x2*x3 + x3^3 - x3","x2*x3 + x2 - x3^2 - 2*x3 + 1","x2^2*x3 + x2^2 - x2*x3^2 - 3*x2*x3 + 2*x3","x1*x2*x3 + x1*x2 - 2*x1*x3 - x2^2*x3 - x2^2 + x2*x3^2 + 2*x2*x3 - x2","x1*x2*x3 + x1*x2 - 2*x1*x3 - x2*x3 - x2 + x3^2 + 2*x3 - 1","x1*x3 - x2","x3 + 1","2*x2 - x3 - 1","2*x1*x2*x3 - x1*x3^2 - x1*x3 - x2^2*x3 - x2^2 + x2*x3^2 + x2*x3","x1*x3 - x3 - 1","x2 - x3 - 1","x2^2 - 2*x2*x3 + x3","x1*x2*x3 - x1*x3 - x2^2 + x2*x3"],"matrix":[["1","1","0","1","1","1","0","x3","x3","0","1"],["0","1","1","x1","1","x2","0","x2","x2","x3^2 - 1","x2"],["0","0","0","0","1","x2","1","x3","-x2*x3 + x3^2 + x3","x2*x3 + x2 - 2*x3","x3"]]}}