# Stored data for abelian variety isogeny class 2.9.ai_bh, downloaded from the LMFDB on 16 October 2025.
{"abvar_count": 35, "abvar_counts": [35, 6825, 580160, 44342025, 3500486675, 282375475200, 22878365334755, 1853317902297225, 150101800979654720, 12157496427346895625], "abvar_counts_str": "35 6825 580160 44342025 3500486675 282375475200 22878365334755 1853317902297225 150101800979654720 12157496427346895625 ", "angle_corank": 1, "angle_rank": 1, "angles": [0.186429498677337, 0.333333333333333], "center_dim": 4, "curve_count": 2, "curve_counts": [2, 84, 794, 6756, 59282, 531342, 4783298, 43053636, 387438986, 3486735924], "curve_counts_str": "2 84 794 6756 59282 531342 4783298 43053636 387438986 3486735924 ", "curves": ["y^2=2*a*x^6+a*x^5+2*a*x^4+2*x^3+2*a*x^2+a*x+2*a"], "dim1_distinct": 2, "dim1_factors": 2, "dim2_distinct": 0, "dim2_factors": 0, "dim3_distinct": 0, "dim3_factors": 0, "dim4_distinct": 0, "dim4_factors": 0, "dim5_distinct": 0, "dim5_factors": 0, "g": 2, "galois_groups": ["2T1", "2T1"], "geom_dim1_distinct": 2, "geom_dim1_factors": 2, "geom_dim2_distinct": 0, "geom_dim2_factors": 0, "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": 3, "geometric_extension_degree": 3, "geometric_galois_groups": ["1T1", "2T1"], "geometric_number_fields": ["1.1.1.1", "2.0.11.1"], "geometric_splitting_field": "2.0.11.1", "geometric_splitting_polynomials": [[3, -1, 1]], "has_geom_ss_factor": true, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 1, "is_geometrically_simple": false, "is_geometrically_squarefree": true, "is_primitive": true, "is_simple": false, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 1, "label": "2.9.ai_bh", "max_divalg_dim": 1, "max_geom_divalg_dim": 4, "max_twist_degree": 12, "newton_coelevation": 1, "newton_elevation": 1, "number_fields": ["2.0.11.1", "2.0.3.1"], "p": 3, "p_rank": 1, "p_rank_deficit": 1, "poly": [1, -8, 33, -72, 81], "poly_str": "1 -8 33 -72 81 ", "primitive_models": [], "q": 9, "real_poly": [1, -8, 15], "simple_distinct": ["1.9.af", "1.9.ad"], "simple_factors": ["1.9.afA", "1.9.adA"], "simple_multiplicities": [1, 1], "slopes": ["0A", "1/2A", "1/2B", "1A"], "splitting_field": "4.0.1089.1", "splitting_polynomials": [[9, -3, -2, -1, 1]], "twist_count": 10, "twists": [["2.9.ac_d", "2.81.c_dv", 2], ["2.9.c_d", "2.81.c_dv", 2], ["2.9.i_bh", "2.81.c_dv", 2], ["2.9.b_am", "2.729.cm_cyw", 3], ["2.9.al_bw", "2.531441.adw_acaeqk", 6], ["2.9.ab_am", "2.531441.adw_acaeqk", 6], ["2.9.l_bw", "2.531441.adw_acaeqk", 6], ["2.9.af_s", "2.282429536481.aeaybk_grsriusos", 12], ["2.9.f_s", "2.282429536481.aeaybk_grsriusos", 12]]}