# Stored data for abelian variety isogeny class 3.4.ac_ad_q, downloaded from the LMFDB on 25 September 2025.
{"abvar_count": 32, "abvar_counts": [32, 2176, 366752, 16720384, 1116666272, 67360606336, 4412606830496, 283955526436864, 18125064065233568, 1157802278727846016], "abvar_counts_str": "32 2176 366752 16720384 1116666272 67360606336 4412606830496 283955526436864 18125064065233568 1157802278727846016 ", "angle_corank": 1, "angle_rank": 2, "angles": [0.119844691139537, 0.314955599330751, 0.934800290470288], "center_dim": 6, "curve_count": 3, "curve_counts": [3, 7, 87, 255, 1063, 4015, 16439, 66111, 263751, 1053007], "curve_counts_str": "3 7 87 255 1063 4015 16439 66111 263751 1053007 ", "curves": ["x^3*y+x^3*z+x*y^3+x*z^3+y^4", "x^4+a^2*x^2*y^2+a^2*x^2*y*z+a*x^2*z^2+x*y*z^2+x*z^3+y^3*z", "x^4+a*x^2*y^2+a*x^2*y*z+a^2*x^2*z^2+x*y*z^2+x*z^3+y^3*z", "y^2+(a*x^3+a*x^2)*y=(a+1)*x^7+(a+1)*x+a+1"], "dim1_distinct": 0, "dim1_factors": 0, "dim2_distinct": 0, "dim2_factors": 0, "dim3_distinct": 1, "dim3_factors": 1, "dim4_distinct": 0, "dim4_factors": 0, "dim5_distinct": 0, "dim5_factors": 0, "g": 3, "galois_groups": ["6T3"], "geom_dim1_distinct": 0, "geom_dim1_factors": 0, "geom_dim2_distinct": 0, "geom_dim2_factors": 0, "geom_dim3_distinct": 1, "geom_dim3_factors": 1, "geom_dim4_distinct": 0, "geom_dim4_factors": 0, "geom_dim5_distinct": 0, "geom_dim5_factors": 0, "geometric_center_dim": 6, "geometric_extension_degree": 1, "geometric_galois_groups": ["6T3"], "geometric_number_fields": ["6.0.399424.1"], "geometric_splitting_field": "6.0.399424.1", "geometric_splitting_polynomials": [[8, -8, 6, -6, 3, -2, 1]], "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 1, "is_geometrically_simple": true, "is_geometrically_squarefree": true, "is_primitive": false, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 4, "label": "3.4.ac_ad_q", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 4, "newton_coelevation": 3, "newton_elevation": 1, "number_fields": ["6.0.399424.1"], "p": 2, "p_rank": 2, "p_rank_deficit": 1, "poly": [1, -2, -3, 16, -12, -32, 64], "poly_str": "1 -2 -3 16 -12 -32 64 ", "primitive_models": ["3.2.a_ab_ac", "3.2.a_ab_c"], "q": 4, "real_poly": [1, -2, -15, 32], "simple_distinct": ["3.4.ac_ad_q"], "simple_factors": ["3.4.ac_ad_qA"], "simple_multiplicities": [1], "slopes": ["0A", "0B", "1/2A", "1/2B", "1A", "1B"], "splitting_field": "6.0.399424.1", "splitting_polynomials": [[8, -8, 6, -6, 3, -2, 1]], "twist_count": 4, "twists": [["3.4.c_ad_aq", "3.16.ak_bx_ahc", 2], ["3.4.ae_n_abc", "3.256.ac_ld_abg", 4], ["3.4.e_n_bc", "3.256.ac_ld_abg", 4]]}