# Stored data for abelian variety isogeny class 3.2.ac_e_af, downloaded from the LMFDB on 09 November 2025.
{"abvar_count": 6, "abvar_counts": [6, 216, 504, 7344, 39666, 217728, 2606694, 20225376, 116867016, 958171896], "abvar_counts_str": "6 216 504 7344 39666 217728 2606694 20225376 116867016 958171896 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 0, "angle_rank": 3, "angles": [0.197201053960792, 0.384973271918692, 0.652365995579139], "center_dim": 6, "cohen_macaulay_max": 1, "curve_count": 1, "curve_counts": [1, 9, 10, 25, 41, 54, 155, 305, 442, 909], "curve_counts_str": "1 9 10 25 41 54 155 305 442 909 ", "curves": ["y^2+(x^4+x^2+x)*y=x^8+x^7+x^5+x^4+x"], "dim1_distinct": 1, "dim1_factors": 1, "dim2_distinct": 1, "dim2_factors": 1, "dim3_distinct": 0, "dim3_factors": 0, "dim4_distinct": 0, "dim4_factors": 0, "dim5_distinct": 0, "dim5_factors": 0, "endomorphism_ring_count": 2, "g": 3, "galois_groups": ["2T1", "4T3"], "geom_dim1_distinct": 1, "geom_dim1_factors": 1, "geom_dim2_distinct": 1, "geom_dim2_factors": 1, "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": 6, "geometric_extension_degree": 1, "geometric_galois_groups": ["2T1", "4T3"], "geometric_number_fields": ["2.0.7.1", "4.0.2873.1"], "geometric_splitting_field": "8.0.19818163729.1", "geometric_splitting_polynomials": [[36, 6, -31, -38, 32, -10, 10, -2, 1]], "group_structure_count": 1, "has_geom_ss_factor": false, "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": "3.2.ac_e_af", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 2, "newton_coelevation": 4, "newton_elevation": 0, "number_fields": ["2.0.7.1", "4.0.2873.1"], "p": 2, "p_rank": 3, "p_rank_deficit": 0, "pic_prime_gens": [[1, 2, 1, 4]], "poly": [1, -2, 4, -5, 8, -8, 8], "poly_str": "1 -2 4 -5 8 -8 8 ", "primitive_models": [], "principal_polarization_count": 3, "q": 2, "real_poly": [1, -2, -2, 3], "simple_distinct": ["1.2.ab", "2.2.ab_b"], "simple_factors": ["1.2.abA", "2.2.ab_bA"], "simple_multiplicities": [1, 1], "singular_primes": ["3,10*F^3-F^2+2*F+3"], "size": 5, "slopes": ["0A", "0B", "0C", "1A", "1B", "1C"], "splitting_field": "8.0.19818163729.1", "splitting_polynomials": [[36, 6, -31, -38, 32, -10, 10, -2, 1]], "twist_count": 4, "twists": [["3.2.a_c_ad", "3.4.e_m_x", 2], ["3.2.a_c_d", "3.4.e_m_x", 2], ["3.2.c_e_f", "3.4.e_m_x", 2]], "weak_equivalence_count": 2, "zfv_index": 9, "zfv_index_factorization": [[3, 2]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_pic_size": 4, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 119, "zfv_singular_count": 2, "zfv_singular_primes": ["3,10*F^3-F^2+2*F+3"]}