# Stored data for abelian variety isogeny class 4.3.ab_d_af_q, downloaded from the LMFDB on 16 April 2026.
{"abvar_count": 80, "abvar_counts": [80, 14080, 396080, 68710400, 3844000000, 261482510080, 23767175392880, 1897727379046400, 151706966810040080, 12116859741184000000], "abvar_counts_str": "80 14080 396080 68710400 3844000000 261482510080 23767175392880 1897727379046400 151706966810040080 12116859741184000000 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 2, "angle_rank": 2, "angles": [0.172732979143934, 0.335169663345628, 0.627267020856067, 0.735169663345628], "center_dim": 8, "cohen_macaulay_max": 3, "curve_count": 3, "curve_counts": [3, 15, 21, 119, 268, 675, 2271, 6719, 19893, 58850], "curve_counts_str": "3 15 21 119 268 675 2271 6719 19893 58850 ", "curves": ["y^2=2*x^10+2*x^9+x^5+x^2+2*x", "x*y+t^2=y^3+x^2*z-y^2*z+y*z^2+z^3+x*y*t+y^2*t=0"], "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": 16, "g": 4, "galois_groups": ["8T10"], "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": 5, "geometric_galois_groups": ["4T3"], "geometric_number_fields": ["4.0.1525.1"], "geometric_splitting_field": "4.0.1525.1", "geometric_splitting_polynomials": [[5, -5, 6, -2, 1]], "group_structure_count": 5, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 1, "is_cyclic": false, "is_geometrically_simple": false, "is_geometrically_squarefree": false, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 2, "label": "4.3.ab_d_af_q", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 30, "newton_coelevation": 6, "newton_elevation": 0, "noncyclic_primes": [2], "number_fields": ["8.0.58140625.2"], "p": 3, "p_rank": 4, "p_rank_deficit": 0, "pic_prime_gens": [[1, 5, 1, 10], [1, 11, 1, 10]], "poly": [1, -1, 3, -5, 16, -15, 27, -27, 81], "poly_str": "1 -1 3 -5 16 -15 27 -27 81 ", "primitive_models": [], "principal_polarization_count": 25, "q": 3, "real_poly": [1, -1, -9, 4, 16], "simple_distinct": ["4.3.ab_d_af_q"], "simple_factors": ["4.3.ab_d_af_qA"], "simple_multiplicities": [1], "singular_primes": ["11,F^4+F^3+27*F^2+6*V^3+18*V^2-3*V+34", "2,F^3-4*F^2+F-V^3+2*V-1"], "size": 102, "slopes": ["0A", "0B", "0C", "0D", "1A", "1B", "1C", "1D"], "splitting_field": "8.0.58140625.2", "splitting_polynomials": [[25, -25, -10, 5, 11, -7, 4, -3, 1]], "twist_count": 10, "twists": [["4.3.b_d_f_q", "4.9.f_bf_dr_om", 2], ["4.3.ag_x_aci_er", "4.243.y_hg_jkq_ksyo", 5], ["4.3.e_d_ak_abd", "4.243.y_hg_jkq_ksyo", 5], ["4.3.ae_d_k_abd", "4.59049.ahs_gcoy_abvcyfw_bibcvuda", 10], ["4.3.a_f_a_n", "4.59049.ahs_gcoy_abvcyfw_bibcvuda", 10], ["4.3.g_x_ci_er", "4.59049.ahs_gcoy_abvcyfw_bibcvuda", 10], ["4.3.d_c_d_n", "4.14348907.bcqy_plkbxc_fmrvuofbk_bkfobdtsvvoo", 15], ["4.3.a_af_a_n", "4.3486784401.jxzk_czkohczs_ojxodrvxtkq_cfzfanqnrjgurmk", 20], ["4.3.ad_c_ad_n", "4.205891132094649.ascoqa_adsmjphgqhfg_ihfwgqqthawdnga_ihgdtzbnjpekccadimbjy", 30]], "weak_equivalence_count": 24, "zfv_index": 704, "zfv_index_factorization": [[2, 6], [11, 1]], "zfv_is_bass": false, "zfv_is_maximal": false, "zfv_pic_size": 20, "zfv_plus_index": 4, "zfv_plus_index_factorization": [[2, 2]], "zfv_plus_norm": 1936, "zfv_singular_count": 4, "zfv_singular_primes": ["11,F^4+F^3+27*F^2+6*V^3+18*V^2-3*V+34", "2,F^3-4*F^2+F-V^3+2*V-1"]}