# Stored data for abelian variety isogeny class 4.3.a_ad_a_q, downloaded from the LMFDB on 15 October 2025.
{"abvar_count": 68, "abvar_counts": [68, 4624, 558416, 75759616, 3500901188, 311828429056, 22843853842052, 1842824173584384, 150114176630072912, 12256309128139811344], "abvar_counts_str": "68 4624 558416 75759616 3500901188 311828429056 22843853842052 1842824173584384 150114176630072912 12256309128139811344 ", "angle_corank": 2, "angle_rank": 2, "angles": [0.148854628963357, 0.264917483542027, 0.735082516457973, 0.851145371036643], "center_dim": 8, "cohen_macaulay_max": 1, "curve_count": 4, "curve_counts": [4, 4, 28, 128, 244, 802, 2188, 6528, 19684, 59524], "curve_counts_str": "4 4 28 128 244 802 2188 6528 19684 59524 ", "curves": [], "dim1_distinct": 0, "dim1_factors": 0, "dim2_distinct": 0, "dim2_factors": 0, "dim3_distinct": 0, "dim3_factors": 0, "dim4_distinct": 1, "dim4_factors": 1, "dim5_distinct": 0, "dim5_factors": 0, "endomorphism_ring_count": 7, "g": 4, "galois_groups": ["8T9"], "geom_dim1_distinct": 0, "geom_dim1_factors": 0, "geom_dim2_distinct": 1, "geom_dim2_factors": 2, "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": 4, "geometric_extension_degree": 2, "geometric_galois_groups": ["4T3"], "geometric_number_fields": ["4.0.3757.1"], "geometric_splitting_field": "4.0.2873.1", "geometric_splitting_polynomials": [[4, -2, 1, -1, 1]], "group_structure_count": 2, "has_geom_ss_factor": false, "has_jacobian": -1, "has_principal_polarization": 1, "hyp_count": 0, "is_geometrically_simple": false, "is_geometrically_squarefree": false, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 0, "label": "4.3.a_ad_a_q", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 12, "newton_coelevation": 6, "newton_elevation": 0, "number_fields": ["8.0.3613452544.3"], "p": 3, "p_rank": 4, "p_rank_deficit": 0, "poly": [1, 0, -3, 0, 16, 0, -27, 0, 81], "poly_str": "1 0 -3 0 16 0 -27 0 81 ", "primitive_models": [], "q": 3, "real_poly": [1, 0, -15, 0, 52], "simple_distinct": ["4.3.a_ad_a_q"], "simple_factors": ["4.3.a_ad_a_qA"], "simple_multiplicities": [1], "singular_primes": ["2,-4*F^2-F-2*V^2+2*V+5"], "slopes": ["0A", "0B", "0C", "0D", "1A", "1B", "1C", "1D"], "splitting_field": "8.0.2113057024.3", "splitting_polynomials": [[16, 0, -4, 0, 5, 0, -1, 0, 1]], "twist_count": 6, "twists": [["4.3.ac_f_ak_bc", "4.81.bu_bob_wyg_jjdk", 4], ["4.3.a_d_a_q", "4.81.bu_bob_wyg_jjdk", 4], ["4.3.c_f_k_bc", "4.81.bu_bob_wyg_jjdk", 4], ["4.3.ab_ab_e_ai", "4.531441.hc_abmuiu_cxbhqu_dihbkpmju", 12], ["4.3.b_ab_ae_ai", "4.531441.hc_abmuiu_cxbhqu_dihbkpmju", 12]], "weak_equivalence_count": 7, "zfv_index": 64, "zfv_index_factorization": [[2, 6]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_plus_index": 2, "zfv_plus_index_factorization": [[2, 1]], "zfv_plus_norm": 256, "zfv_singular_count": 2, "zfv_singular_primes": ["2,-4*F^2-F-2*V^2+2*V+5"]}