# Stored data for abelian variety isogeny class 3.2.ac_c_ad, downloaded from the LMFDB on 01 July 2026.
{"abvar_count": 2, "abvar_counts": [2, 56, 224, 4144, 16522, 175616, 2570626, 16783200, 133677152, 1073731736], "abvar_counts_str": "2 56 224 4144 16522 175616 2570626 16783200 133677152 1073731736 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 2, "angle_rank": 1, "angles": [0.0516399385853587, 0.384973271918692, 0.718306605252025], "center_dim": 6, "cohen_macaulay_max": 1, "curve_count": 1, "curve_counts": [1, 5, 4, 17, 11, 38, 155, 257, 508, 1025], "curve_counts_str": "1 5 4 17 11 38 155 257 508 1025 ", "curves": ["y^2+(x^4+x^2+x)*y=x^8+x^6+x^4+x^3+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", "4T2"], "geom_dim1_distinct": 1, "geom_dim1_factors": 3, "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": 2, "geometric_extension_degree": 6, "geometric_galois_groups": ["2T1"], "geometric_number_fields": ["2.0.7.1"], "geometric_splitting_field": "2.0.7.1", "geometric_splitting_polynomials": [[2, -1, 1]], "group_structure_count": 1, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 1, "is_cyclic": true, "is_geometrically_simple": false, "is_geometrically_squarefree": false, "is_primitive": true, "is_simple": false, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 1, "label": "3.2.ac_c_ad", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 42, "newton_coelevation": 4, "newton_elevation": 0, "noncyclic_primes": [], "number_fields": ["2.0.7.1", "4.0.441.1"], "p": 2, "p_rank": 3, "p_rank_deficit": 0, "pic_prime_gens": [], "poly": [1, -2, 2, -3, 4, -8, 8], "poly_str": "1 -2 2 -3 4 -8 8 ", "primitive_models": [], "principal_polarization_count": 1, "q": 2, "real_poly": [1, -2, -4, 5], "simple_distinct": ["1.2.ab", "2.2.ab_ab"], "simple_factors": ["1.2.abA", "2.2.ab_abA"], "simple_multiplicities": [1, 1], "singular_primes": ["5,9*F^3+7*F^2+2*F-10*V+7"], "size": 2, "slopes": ["0A", "0B", "0C", "1A", "1B", "1C"], "splitting_field": "4.0.441.1", "splitting_polynomials": [[4, -2, -1, -1, 1]], "twist_count": 14, "twists": [["3.2.a_a_af", "3.4.a_a_aj", 2], ["3.2.a_a_f", "3.4.a_a_aj", 2], ["3.2.c_c_d", "3.4.a_a_aj", 2], ["3.2.b_f_d", "3.8.af_ab_bt", 3], ["3.2.ad_j_an", "3.64.abb_qt_agez", 6], ["3.2.ab_f_ad", "3.64.abb_qt_agez", 6], ["3.2.d_j_n", "3.64.abb_qt_agez", 6], ["3.2.ab_ab_d", "3.4096.fl_bbzn_ctqhb", 12], ["3.2.b_ab_ad", "3.4096.fl_bbzn_ctqhb", 12], ["3.2.ae_j_ap", "3.4398046511104.axtmzj_jrfguzykil_acfoofcbglfpqnwj", 42], ["3.2.ad_c_b", "3.4398046511104.axtmzj_jrfguzykil_acfoofcbglfpqnwj", 42], ["3.2.d_c_ab", "3.4398046511104.axtmzj_jrfguzykil_acfoofcbglfpqnwj", 42], ["3.2.e_j_p", "3.4398046511104.axtmzj_jrfguzykil_acfoofcbglfpqnwj", 42]], "weak_equivalence_count": 2, "zfv_index": 25, "zfv_index_factorization": [[5, 2]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_pic_size": 1, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 7, "zfv_singular_count": 2, "zfv_singular_primes": ["5,9*F^3+7*F^2+2*F-10*V+7"]}