# Stored data for abelian variety isogeny class 3.8.ak_bu_afp, downloaded from the LMFDB on 28 April 2024.
{"label": "3.8.ak_bu_afp", "g": 3, "p": 2, "q": 8, "poly": [1, -10, 46, -145, 368, -640, 512], "poly_str": "1 -10 46 -145 368 -640 512 ", "slopes": ["0A", "0B", "0C", "1A", "1B", "1C"], "p_rank": 3, "p_rank_deficit": 0, "angles": [0.0644257339288952, 0.154919815756076, 0.530510095142127], "angle_rank": 3, "number_fields": ["2.0.7.1", "4.0.56129.1"], "galois_groups": ["2T1", "4T3"], "center_dim": 6, "abvar_counts": [132, 227304, 120901968, 66087728784, 35454761137092, 18117804070485504, 9225792679711059276, 4722501843678479968800, 2418408465528152650653936, 1238004920384797262662536264], "abvar_counts_str": "132 227304 120901968 66087728784 35454761137092 18117804070485504 9225792679711059276 4722501843678479968800 2418408465528152650653936 1238004920384797262662536264 ", "abvar_count": 132, "curve_counts": [-1, 57, 458, 3937, 33019, 263646, 2097703, 16777697, 134248634, 1073798097], "curve_counts_str": "-1 57 458 3937 33019 263646 2097703 16777697 134248634 1073798097 ", "curve_count": -1, "has_jacobian": -1, "has_principal_polarization": 1, "geometric_extension_degree": 1, "geometric_center_dim": 6, "geometric_number_fields": ["2.0.7.1", "4.0.56129.1"], "geometric_galois_groups": ["2T1", "4T3"], "primitive_models": [], "is_primitive": true, "twists": [["3.8.a_ae_ap", "3.64.ai_abw_bop", 2], ["3.8.a_ae_p", "3.64.ai_abw_bop", 2], ["3.8.k_bu_fp", "3.64.ai_abw_bop", 2]], "twist_count": 4, "max_twist_degree": 2, "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "is_simple": false, "is_geometrically_simple": false, "simple_distinct": ["1.8.af", "2.8.af_n"], "simple_multiplicities": [1, 1], "simple_factors": ["1.8.afA", "2.8.af_nA"], "dim1_factors": 1, "dim2_factors": 1, "dim3_factors": 0, "dim4_factors": 0, "dim5_factors": 0, "dim1_distinct": 1, "dim2_distinct": 1, "dim3_distinct": 0, "dim4_distinct": 0, "dim5_distinct": 0, "geom_dim1_factors": 1, "geom_dim2_factors": 1, "geom_dim3_factors": 0, "geom_dim4_factors": 0, "geom_dim5_factors": 0, "geom_dim1_distinct": 1, "geom_dim2_distinct": 1, "geom_dim3_distinct": 0, "geom_dim4_distinct": 0, "geom_dim5_distinct": 0, "has_geom_ss_factor": false, "real_poly": [1, -10, 22, 15], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_index": 9, "zfv_index_factorization": [[3, 2]], "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 287, "geometric_splitting_field": "8.0.7564265603041.1", "splitting_field": "8.0.7564265603041.1", "geometric_splitting_polynomials": [[1232, 1008, 235, -68, 54, 24, 16, -2, 1]], "splitting_polynomials": [[1232, 1008, 235, -68, 54, 24, 16, -2, 1]], "is_squarefree": true, "is_geometrically_squarefree": true, "size": 15, "principal_polarization_count": 9, "pic_prime_gens": [[1, 2, 1, 4], [2, 3, 1, 3]]}