# Stored data for abelian variety isogeny class 3.2.ac_e_ae, downloaded from the LMFDB on 01 July 2026.
{"abvar_count": 7, "abvar_counts": [7, 245, 637, 11025, 43337, 156065, 1865969, 16769025, 125599201, 1145180225], "abvar_counts_str": "7 245 637 11025 43337 156065 1865969 16769025 125599201 1145180225 ", "angle_corank": 3, "angle_rank": 0, "angles": [0.25, 0.333333333333333, 0.666666666666667], "center_dim": 6, "cohen_macaulay_max": 2, "curve_count": 1, "curve_counts": [1, 9, 13, 33, 41, 33, 113, 257, 481, 1089], "curve_counts_str": "1 9 13 33 41 33 113 257 481 1089 ", "curves": [], "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": 4, "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": 1, "geometric_extension_degree": 24, "geometric_galois_groups": ["1T1"], "geometric_number_fields": ["1.1.1.1"], "geometric_splitting_field": "1.1.1.1", "geometric_splitting_polynomials": [[0, 1]], "group_structure_count": 1, "has_geom_ss_factor": true, "has_jacobian": -1, "has_principal_polarization": 1, "hyp_count": 0, "is_cyclic": true, "is_geometrically_simple": false, "is_geometrically_squarefree": false, "is_primitive": true, "is_simple": false, "is_squarefree": true, "is_supersingular": true, "jacobian_count": 0, "label": "3.2.ac_e_ae", "max_divalg_dim": 1, "max_geom_divalg_dim": 4, "max_twist_degree": 24, "newton_coelevation": 0, "newton_elevation": 4, "noncyclic_primes": [], "number_fields": ["2.0.4.1", "4.0.576.2"], "p": 2, "p_rank": 0, "p_rank_deficit": 3, "poly": [1, -2, 4, -4, 8, -8, 8], "poly_str": "1 -2 4 -4 8 -8 8 ", "primitive_models": [], "q": 2, "real_poly": [1, -2, -2, 4], "simple_distinct": ["1.2.ac", "2.2.a_c"], "simple_factors": ["1.2.acA", "2.2.a_cA"], "simple_multiplicities": [1, 1], "singular_primes": ["2,F^3+9*F+7*V-6,-3*F^2-3*V^2+V"], "slopes": ["1/2A", "1/2B", "1/2C", "1/2D", "1/2E", "1/2F"], "splitting_field": "8.0.5308416.1", "splitting_polynomials": [[1, 0, 0, 0, -1, 0, 0, 0, 1]], "twist_count": 25, "twists": [["3.2.c_e_e", "3.4.e_q_bg", 2], ["3.2.ac_ac_i", "3.8.e_ai_acm", 3], ["3.2.ac_a_e", "3.16.q_ey_yq", 4], ["3.2.c_a_ae", "3.16.q_ey_yq", 4], ["3.2.c_e_e", "3.16.q_ey_yq", 4], ["3.2.ac_ac_i", "3.64.abg_rg_agbo", 6], ["3.2.c_ac_ai", "3.64.abg_rg_agbo", 6], ["3.2.c_e_e", "3.64.abg_rg_agbo", 6], ["3.2.ae_i_am", "3.256.a_a_amdc", 8], ["3.2.ac_e_ai", "3.256.a_a_amdc", 8], ["3.2.a_a_ae", "3.256.a_a_amdc", 8], ["3.2.a_a_a", "3.256.a_a_amdc", 8], ["3.2.a_a_e", "3.256.a_a_amdc", 8], ["3.2.a_e_a", "3.256.a_a_amdc", 8], ["3.2.c_e_i", "3.256.a_a_amdc", 8], ["3.2.e_i_m", "3.256.a_a_amdc", 8], ["3.2.ac_a_e", "3.4096.aey_agbo_chrdw", 12], ["3.2.ac_g_ai", "3.4096.aey_agbo_chrdw", 12], ["3.2.c_a_ae", "3.4096.aey_agbo_chrdw", 12], ["3.2.c_g_i", "3.4096.aey_agbo_chrdw", 12], ["3.2.ag_s_abg", "3.16777216.abkjg_veshnc_agpdbywrmu", 24], ["3.2.ae_i_am", "3.16777216.abkjg_veshnc_agpdbywrmu", 24], ["3.2.ae_k_aq", "3.16777216.abkjg_veshnc_agpdbywrmu", 24], ["3.2.ac_ac_i", "3.16777216.abkjg_veshnc_agpdbywrmu", 24], ["3.2.ac_a_e", "3.16777216.abkjg_veshnc_agpdbywrmu", 24], ["3.2.ac_c_a", "3.16777216.abkjg_veshnc_agpdbywrmu", 24], ["3.2.ac_e_ai", "3.16777216.abkjg_veshnc_agpdbywrmu", 24], ["3.2.ac_g_ai", "3.16777216.abkjg_veshnc_agpdbywrmu", 24], ["3.2.a_ac_a", "3.16777216.abkjg_veshnc_agpdbywrmu", 24], ["3.2.a_a_ae", "3.16777216.abkjg_veshnc_agpdbywrmu", 24], ["3.2.a_a_a", "3.16777216.abkjg_veshnc_agpdbywrmu", 24], ["3.2.a_a_e", "3.16777216.abkjg_veshnc_agpdbywrmu", 24], ["3.2.a_c_a", "3.16777216.abkjg_veshnc_agpdbywrmu", 24], ["3.2.a_e_a", "3.16777216.abkjg_veshnc_agpdbywrmu", 24], ["3.2.a_g_a", "3.16777216.abkjg_veshnc_agpdbywrmu", 24], ["3.2.c_ac_ai", "3.16777216.abkjg_veshnc_agpdbywrmu", 24], ["3.2.c_a_ae", "3.16777216.abkjg_veshnc_agpdbywrmu", 24], ["3.2.c_c_a", "3.16777216.abkjg_veshnc_agpdbywrmu", 24], ["3.2.c_e_e", "3.16777216.abkjg_veshnc_agpdbywrmu", 24], ["3.2.c_e_i", "3.16777216.abkjg_veshnc_agpdbywrmu", 24], ["3.2.c_g_i", "3.16777216.abkjg_veshnc_agpdbywrmu", 24], ["3.2.e_i_m", "3.16777216.abkjg_veshnc_agpdbywrmu", 24], ["3.2.e_k_q", "3.16777216.abkjg_veshnc_agpdbywrmu", 24], ["3.2.g_s_bg", "3.16777216.abkjg_veshnc_agpdbywrmu", 24]], "weak_equivalence_count": 5, "zfv_index": 8, "zfv_index_factorization": [[2, 3]], "zfv_is_bass": false, "zfv_is_maximal": false, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 144, "zfv_singular_count": 3, "zfv_singular_primes": ["2,F^3+9*F+7*V-6,-3*F^2-3*V^2+V"]}