# Stored data for abelian variety isogeny class 2.16.ai_bj, downloaded from the LMFDB on 04 May 2024.
{"label": "2.16.ai_bj", "g": 2, "p": 2, "q": 16, "poly": [1, -8, 35, -128, 256], "poly_str": "1 -8 35 -128 256 ", "slopes": ["0A", "0B", "1A", "1B"], "p_rank": 2, "p_rank_deficit": 0, "angles": [0.100372839388751, 0.484299017784308], "angle_rank": 2, "number_fields": ["4.0.66417.2"], "galois_groups": ["4T3"], "center_dim": 4, "abvar_counts": [156, 66768, 16554564, 4252053312, 1099002013356, 281649882685392, 72065800325865684, 18446682900457813248, 4722385389546620728764, 1208930156277080585728848], "abvar_counts_str": "156 66768 16554564 4252053312 1099002013356 281649882685392 72065800325865684 18446682900457813248 4722385389546620728764 1208930156277080585728848 ", "abvar_count": 156, "curve_counts": [9, 263, 4041, 64879, 1048089, 16787639, 268466025, 4294953055, 68719751865, 1099515571943], "curve_counts_str": "9 263 4041 64879 1048089 16787639 268466025 4294953055 68719751865 1099515571943 ", "curve_count": 9, "has_jacobian": 1, "has_principal_polarization": 1, "geometric_extension_degree": 1, "geometric_center_dim": 4, "geometric_number_fields": ["4.0.66417.2"], "geometric_galois_groups": ["4T3"], "primitive_models": [], "is_primitive": true, "twists": [["2.16.i_bj", "2.256.g_alz", 2]], "twist_count": 2, "max_twist_degree": 2, "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "is_simple": true, "is_geometrically_simple": true, "simple_distinct": ["2.16.ai_bj"], "simple_multiplicities": [1], "simple_factors": ["2.16.ai_bjA"], "dim1_factors": 0, "dim2_factors": 1, "dim3_factors": 0, "dim4_factors": 0, "dim5_factors": 0, "dim1_distinct": 0, "dim2_distinct": 1, "dim3_distinct": 0, "dim4_distinct": 0, "dim5_distinct": 0, "geom_dim1_factors": 0, "geom_dim2_factors": 1, "geom_dim3_factors": 0, "geom_dim4_factors": 0, "geom_dim5_factors": 0, "geom_dim1_distinct": 0, "geom_dim2_distinct": 1, "geom_dim3_distinct": 0, "geom_dim4_distinct": 0, "geom_dim5_distinct": 0, "has_geom_ss_factor": false, "real_poly": [1, -8, 3], "jacobian_count": 16, "curves": ["y^2+(x^2+x+a^3+a^2+a+1)*y=(a+1)*x^5+a^3*x^4+a*x^3+a^3*x^2+(a+1)*x", "y^2+(x^2+x+a^3+a)*y=(a^2+1)*x^5+(a^3+1)*x^4+a^2*x^3+(a^3+1)*x^2+(a^2+1)*x+a^3+a^2+a", "y^2+(x^2+x+a^3)*y=a*x^5+(a^3+a^2+1)*x^4+(a+1)*x^3+(a^3+a^2+1)*x^2+a*x+a^3+a+1", "y^2+(x^2+x+a^3+a+1)*y=(a^2+a)*x^5+(a^3+1)*x^4+(a^2+1)*x^3+(a^3+1)*x^2+(a^3+a^2+a)*x+a+1", "y^2+(x^2+x+a^3+a^2+1)*y=(a^2+a)*x^5+a^3*x^4+a^2*x^3+a^3*x^2+(a^3+1)*x", "y^2+(x^2+x)*y=a^3*x^5+(a^3+1)*x^3+(a^3+a^2+1)*x^2+(a^3+a^2)*x", "y^2+(x^2+x+a^3)*y=x^5+(a^2+1)*x^3+(a^3+a^2+a)*x+a^2+a", "y^2+(x^2+x+a^3+a^2)*y=a^2*x^5+(a^3+1)*x^4+(a^2+1)*x^3+(a^3+1)*x^2+a^2*x+a", "y^2+(x^2+x+a^3+a^2+a)*y=(a^2+a+1)*x^5+(a^3+a^2+a)*x^4+(a+1)*x^3+(a^3+a^2+a)*x^2+(a^3+a^2+1)*x+a^2+1", "y^2+(x^2+x+a^3+1)*y=(a^2+a+1)*x^5+(a^3+a+1)*x^4+a*x^3+(a^3+a+1)*x^2+(a^3+a+1)*x+a^3+a^2+1", "y^2+(x^2+x+a^3+a)*y=x^5+(a+1)*x^3+(a^3+a^2+1)*x+a^2+a+1", "y^2+(x^2+x)*y=a^3*x^5+a^3*x^4+(a^3+a+1)*x^3+x^2+(a^3+a)*x", "y^2+(x^2+x+a^3+a^2+a+1)*y=x^5+a^2*x^3+(a^3+1)*x+a^2+a", "y^2+(x^2+x)*y=(a^3+a+1)*x^5+(a^3+a+1)*x^4+(a^3+a^2+a)*x^3+a^2*x^2+(a^3+a)*x", "y^2+(x^2+x+a^3+a^2)*y=x^5+a*x^3+(a^3+a+1)*x+a^2+a+1", "y^2+(x^2+x)*y=(a^3+a^2)*x^5+(a^3+a^2+a+1)*x^4+(a^3+a^2+1)*x^3+(a^3+a^2+a)*x"], "hyp_count": 16, "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_index": 4, "zfv_index_factorization": [[2, 2]], "zfv_plus_index": 2, "zfv_plus_index_factorization": [[2, 1]], "zfv_plus_norm": 393, "geometric_splitting_field": "4.0.66417.2", "splitting_field": "4.0.66417.2", "geometric_splitting_polynomials": [[29, -18, 19, -2, 1]], "splitting_polynomials": [[29, -18, 19, -2, 1]], "is_squarefree": true, "is_geometrically_squarefree": true, "size": 24, "principal_polarization_count": 16, "pic_prime_gens": [[1, 3, 1, 2], [1, 13, 1, 12]]}