# Stored data for abelian variety isogeny class 4.2.ae_h_ag_e, downloaded from the LMFDB on 05 May 2024.
{"label": "4.2.ae_h_ag_e", "g": 4, "p": 2, "q": 2, "poly": [1, -4, 7, -6, 4, -12, 28, -32, 16], "poly_str": "1 -4 7 -6 4 -12 28 -32 16 ", "slopes": ["0A", "0B", "1/2A", "1/2B", "1/2C", "1/2D", "1A", "1B"], "p_rank": 2, "p_rank_deficit": 2, "angles": [0.0693533547549937, 0.25, 0.339907131294691, 0.770553776539698], "angle_rank": 2, "number_fields": ["2.0.4.1", "6.0.2580992.1"], "galois_groups": ["2T1", "6T3"], "center_dim": 8, "abvar_counts": [2, 220, 5018, 149600, 686422, 13799500, 237933026, 3753763200, 79235379158, 1121647869100], "abvar_counts_str": "2 220 5018 149600 686422 13799500 237933026 3753763200 79235379158 1121647869100 ", "abvar_count": 2, "curve_counts": [-1, 3, 11, 31, 19, 51, 111, 223, 587, 1043], "curve_counts_str": "-1 3 11 31 19 51 111 223 587 1043 ", "curve_count": -1, "has_jacobian": -1, "has_principal_polarization": 1, "geometric_extension_degree": 4, "geometric_center_dim": 7, "geometric_number_fields": ["1.1.1.1", "6.0.2580992.1"], "geometric_galois_groups": ["1T1", "6T3"], "primitive_models": [], "is_primitive": true, "twists": [["4.2.a_ab_ac_e", "4.4.ac_j_au_bo", 2], ["4.2.a_ab_c_e", "4.4.ac_j_au_bo", 2], ["4.2.e_h_g_e", "4.4.ac_j_au_bo", 2], ["4.2.a_ab_ac_e", "4.16.o_dd_lc_bme", 4], ["4.2.ac_d_ae_e", "4.256.abi_sn_aomq_mfjc", 8], ["4.2.c_d_e_e", "4.256.abi_sn_aomq_mfjc", 8]], "twist_count": 6, "max_twist_degree": 8, "max_divalg_dim": 1, "max_geom_divalg_dim": 4, "is_simple": false, "is_geometrically_simple": false, "simple_distinct": ["1.2.ac", "3.2.ac_b_a"], "simple_multiplicities": [1, 1], "simple_factors": ["1.2.acA", "3.2.ac_b_aA"], "dim1_factors": 1, "dim2_factors": 0, "dim3_factors": 1, "dim4_factors": 0, "dim5_factors": 0, "dim1_distinct": 1, "dim2_distinct": 0, "dim3_distinct": 1, "dim4_distinct": 0, "dim5_distinct": 0, "geom_dim1_factors": 1, "geom_dim2_factors": 0, "geom_dim3_factors": 1, "geom_dim4_factors": 0, "geom_dim5_factors": 0, "geom_dim1_distinct": 1, "geom_dim2_distinct": 0, "geom_dim3_distinct": 1, "geom_dim4_distinct": 0, "geom_dim5_distinct": 0, "has_geom_ss_factor": true, "real_poly": [1, -4, -1, 18, -16], "jacobian_count": 0, "curves": [], "hyp_count": 0, "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_index": 4, "zfv_index_factorization": [[2, 2]], "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 32, "geometric_splitting_field": "6.0.2580992.1", "splitting_field": "12.0.426337261060096.1", "geometric_splitting_polynomials": [[8, -8, 2, 0, 1, -2, 1]], "splitting_polynomials": [[64, 0, 0, -32, -12, 8, 8, 4, -3, -4, 0, 0, 1]], "is_squarefree": true, "is_geometrically_squarefree": true, "size": 3, "principal_polarization_count": 0, "pic_prime_gens": []}