# Stored data for abelian variety isogeny class 4.2.af_m_au_bd, downloaded from the LMFDB on 29 April 2026.
{"abvar_count": 1, "abvar_counts": [1, 211, 1861, 88831, 1046771, 12172801, 344358281, 5598573775, 68193052891, 1095729526441], "abvar_counts_str": "1 211 1861 88831 1046771 12172801 344358281 5598573775 68193052891 1095729526441 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 2, "angle_rank": 2, "angles": [0.0635622003030556, 0.165221137389402, 0.365221137389402, 0.663562200303056], "center_dim": 8, "cohen_macaulay_max": 1, "curve_count": -2, "curve_counts": [-2, 4, 4, 20, 33, 46, 159, 324, 508, 1019], "curve_counts_str": "-2 4 4 20 33 46 159 324 508 1019 ", "curves": [], "dim1_distinct": 0, "dim1_factors": 0, "dim2_distinct": 0, "dim2_factors": 0, "dim3_distinct": 0, "dim3_factors": 0, "dim4_distinct": 1, "dim4_factors": 1, "dim5_distinct": 0, "dim5_factors": 0, "endomorphism_ring_count": 1, "g": 4, "galois_groups": ["8T10"], "geom_dim1_distinct": 0, "geom_dim1_factors": 0, "geom_dim2_distinct": 1, "geom_dim2_factors": 2, "geom_dim3_distinct": 0, "geom_dim3_factors": 0, "geom_dim4_distinct": 0, "geom_dim4_factors": 0, "geom_dim5_distinct": 0, "geom_dim5_factors": 0, "geometric_center_dim": 4, "geometric_extension_degree": 10, "geometric_galois_groups": ["4T3"], "geometric_number_fields": ["4.0.3625.1"], "geometric_splitting_field": "4.0.3625.1", "geometric_splitting_polynomials": [[11, -1, 6, -1, 1]], "group_structure_count": 1, "has_geom_ss_factor": false, "has_jacobian": -1, "has_principal_polarization": 1, "hyp_count": 0, "is_cyclic": true, "is_geometrically_simple": false, "is_geometrically_squarefree": false, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 0, "label": "4.2.af_m_au_bd", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 20, "newton_coelevation": 6, "newton_elevation": 0, "noncyclic_primes": [], "number_fields": ["8.0.13140625.1"], "p": 2, "p_rank": 4, "p_rank_deficit": 0, "pic_prime_gens": [], "poly": [1, -5, 12, -20, 29, -40, 48, -40, 16], "poly_str": "1 -5 12 -20 29 -40 48 -40 16 ", "primitive_models": [], "principal_polarization_count": 1, "q": 2, "real_poly": [1, -5, 4, 10, -11], "simple_distinct": ["4.2.af_m_au_bd"], "simple_factors": ["4.2.af_m_au_bdA"], "simple_multiplicities": [1], "singular_primes": [], "size": 1, "slopes": ["0A", "0B", "0C", "0D", "1A", "1B", "1C", "1D"], "splitting_field": "8.0.13140625.1", "splitting_polynomials": [[1, 3, 5, 3, 4, -3, 5, -3, 1]], "twist_count": 6, "twists": [["4.2.f_m_u_bd", "4.4.ab_c_ai_z", 2], ["4.2.a_ad_a_j", "4.32.a_ad_a_bwv", 5], ["4.2.a_c_af_ab", "4.32.a_ad_a_bwv", 5], ["4.2.a_c_f_ab", "4.32.a_ad_a_bwv", 5], ["4.2.f_m_u_bd", "4.32.a_ad_a_bwv", 5], ["4.2.a_d_a_j", "4.1048576.hmo_bedrtj_czowjfcc_fjyfkiixcb", 20]], "weak_equivalence_count": 1, "zfv_index": 1, "zfv_index_factorization": [], "zfv_is_bass": true, "zfv_is_maximal": true, "zfv_pic_size": 1, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 25, "zfv_singular_count": 0, "zfv_singular_primes": []}