# Stored data for abelian variety isogeny class 4.2.ac_c_e_ai, downloaded from the LMFDB on 16 October 2025.
{"abvar_count": 13, "abvar_counts": [13, 325, 28561, 105625, 1333033, 17850625, 237209713, 3773030625, 53527912321, 1100585370625], "abvar_counts_str": "13 325 28561 105625 1333033 17850625 237209713 3773030625 53527912321 1100585370625 ", "angle_corank": 4, "angle_rank": 0, "angles": [0.25, 0.25, 0.416666666666667, 0.916666666666667], "center_dim": 6, "curve_count": 1, "curve_counts": [1, 5, 25, 25, 41, 65, 113, 225, 385, 1025], "curve_counts_str": "1 5 25 25 41 65 113 225 385 1025 ", "curves": [], "dim1_distinct": 1, "dim1_factors": 2, "dim2_distinct": 1, "dim2_factors": 1, "dim3_distinct": 0, "dim3_factors": 0, "dim4_distinct": 0, "dim4_factors": 0, "dim5_distinct": 0, "dim5_factors": 0, "g": 4, "galois_groups": ["2T1", "4T2"], "geom_dim1_distinct": 1, "geom_dim1_factors": 4, "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": 12, "geometric_galois_groups": ["1T1"], "geometric_number_fields": ["1.1.1.1"], "geometric_splitting_field": "1.1.1.1", "geometric_splitting_polynomials": [[0, 1]], "has_geom_ss_factor": true, "has_jacobian": -1, "has_principal_polarization": 1, "hyp_count": 0, "is_geometrically_simple": false, "is_geometrically_squarefree": false, "is_primitive": true, "is_simple": false, "is_squarefree": false, "is_supersingular": true, "jacobian_count": 0, "label": "4.2.ac_c_e_ai", "max_divalg_dim": 1, "max_geom_divalg_dim": 4, "max_twist_degree": 120, "newton_coelevation": 0, "newton_elevation": 6, "number_fields": ["2.0.4.1", "4.0.144.1"], "p": 2, "p_rank": 0, "p_rank_deficit": 4, "poly": [1, -2, 2, 4, -8, 8, 8, -16, 16], "poly_str": "1 -2 2 4 -8 8 8 -16 16 ", "primitive_models": [], "q": 2, "real_poly": [1, -2, -6, 16, -8], "simple_distinct": ["1.2.ac", "2.2.c_c"], "simple_factors": ["1.2.acA", "1.2.acB", "2.2.c_cA"], "simple_multiplicities": [2, 1], "slopes": ["1/2A", "1/2B", "1/2C", "1/2D", "1/2E", "1/2F", "1/2G", "1/2H"], "splitting_field": "4.0.144.1", "splitting_polynomials": [[1, 0, -1, 0, 1]], "twist_count": 65, "twists": [["4.2.ag_s_abk_ce", "4.4.a_e_a_a", 2], ["4.2.ac_c_ae_i", "4.4.a_e_a_a", 2], ["4.2.c_c_ae_ai", "4.4.a_e_a_a", 2], ["4.2.c_c_e_i", "4.4.a_e_a_a", 2], ["4.2.g_s_bk_ce", "4.4.a_e_a_a", 2], ["4.2.ai_bg_adc_fg", "4.8.q_ey_yq_dfs", 3], ["4.2.e_i_q_bc", "4.8.q_ey_yq_dfs", 3], ["4.2.ae_i_aq_bc", "4.64.a_jw_a_bkjg", 6], ["4.2.ae_i_ai_i", "4.64.a_jw_a_bkjg", 6], ["4.2.a_a_a_ae", "4.64.a_jw_a_bkjg", 6], ["4.2.a_a_a_i", "4.64.a_jw_a_bkjg", 6], ["4.2.e_i_i_i", "4.64.a_jw_a_bkjg", 6], ["4.2.i_bg_dc_fg", "4.64.a_jw_a_bkjg", 6], ["4.2.ae_g_a_ai", "4.256.abg_jw_amdc_oxum", 8], ["4.2.ae_k_au_bg", "4.256.abg_jw_amdc_oxum", 8], ["4.2.ae_k_aq_y", "4.256.abg_jw_amdc_oxum", 8], ["4.2.ac_ac_e_a", "4.256.abg_jw_amdc_oxum", 8], ["4.2.ac_c_a_a", "4.256.abg_jw_amdc_oxum", 8], ["4.2.ac_g_am_q", "4.256.abg_jw_amdc_oxum", 8], ["4.2.ac_g_ai_q", "4.256.abg_jw_amdc_oxum", 8], ["4.2.a_ag_a_q", "4.256.abg_jw_amdc_oxum", 8], ["4.2.a_ac_a_a", "4.256.abg_jw_amdc_oxum", 8], ["4.2.a_ac_a_i", "4.256.abg_jw_amdc_oxum", 8], ["4.2.a_c_ae_a", "4.256.abg_jw_amdc_oxum", 8], ["4.2.a_c_a_a", "4.256.abg_jw_amdc_oxum", 8], ["4.2.a_c_a_i", "4.256.abg_jw_amdc_oxum", 8], ["4.2.a_c_e_a", "4.256.abg_jw_amdc_oxum", 8], ["4.2.a_g_a_q", "4.256.abg_jw_amdc_oxum", 8], ["4.2.c_ac_ae_a", "4.256.abg_jw_amdc_oxum", 8], ["4.2.c_c_a_a", "4.256.abg_jw_amdc_oxum", 8], ["4.2.c_g_i_q", "4.256.abg_jw_amdc_oxum", 8], ["4.2.c_g_m_q", "4.256.abg_jw_amdc_oxum", 8], ["4.2.e_g_a_ai", "4.256.abg_jw_amdc_oxum", 8], ["4.2.e_k_q_y", "4.256.abg_jw_amdc_oxum", 8], ["4.2.e_k_u_bg", "4.256.abg_jw_amdc_oxum", 8], ["4.2.c_c_a_ae", "4.32768.abnk_bdvoy_aoddnrk_eoeqskhs", 15], ["4.2.ag_u_abs_cu", "4.16777216.abwmi_bnnzmhc_asldkrqrue_fjoxzqwbkits", 24], ["4.2.ae_e_i_ay", "4.16777216.abwmi_bnnzmhc_asldkrqrue_fjoxzqwbkits", 24], ["4.2.ae_m_ay_bo", "4.16777216.abwmi_bnnzmhc_asldkrqrue_fjoxzqwbkits", 24], ["4.2.ac_a_a_e", "4.16777216.abwmi_bnnzmhc_asldkrqrue_fjoxzqwbkits", 24], ["4.2.ac_a_e_ai", "4.16777216.abwmi_bnnzmhc_asldkrqrue_fjoxzqwbkits", 24], ["4.2.ac_e_ai_m", "4.16777216.abwmi_bnnzmhc_asldkrqrue_fjoxzqwbkits", 24], ["4.2.ac_e_ae_i", "4.16777216.abwmi_bnnzmhc_asldkrqrue_fjoxzqwbkits", 24], ["4.2.ac_i_am_y", "4.16777216.abwmi_bnnzmhc_asldkrqrue_fjoxzqwbkits", 24], ["4.2.a_ai_a_y", "4.16777216.abwmi_bnnzmhc_asldkrqrue_fjoxzqwbkits", 24], ["4.2.a_ae_a_i", "4.16777216.abwmi_bnnzmhc_asldkrqrue_fjoxzqwbkits", 24], ["4.2.a_ae_a_m", "4.16777216.abwmi_bnnzmhc_asldkrqrue_fjoxzqwbkits", 24], ["4.2.a_a_a_ai", "4.16777216.abwmi_bnnzmhc_asldkrqrue_fjoxzqwbkits", 24], ["4.2.a_a_a_e", "4.16777216.abwmi_bnnzmhc_asldkrqrue_fjoxzqwbkits", 24], ["4.2.a_c_e_a", "4.16777216.abwmi_bnnzmhc_asldkrqrue_fjoxzqwbkits", 24], ["4.2.a_e_a_i", "4.16777216.abwmi_bnnzmhc_asldkrqrue_fjoxzqwbkits", 24], ["4.2.a_e_a_m", "4.16777216.abwmi_bnnzmhc_asldkrqrue_fjoxzqwbkits", 24], ["4.2.a_i_a_y", "4.16777216.abwmi_bnnzmhc_asldkrqrue_fjoxzqwbkits", 24], ["4.2.c_a_ae_ai", "4.16777216.abwmi_bnnzmhc_asldkrqrue_fjoxzqwbkits", 24], ["4.2.c_a_a_e", "4.16777216.abwmi_bnnzmhc_asldkrqrue_fjoxzqwbkits", 24], ["4.2.c_e_e_i", "4.16777216.abwmi_bnnzmhc_asldkrqrue_fjoxzqwbkits", 24], ["4.2.c_e_i_m", "4.16777216.abwmi_bnnzmhc_asldkrqrue_fjoxzqwbkits", 24], ["4.2.c_i_m_y", "4.16777216.abwmi_bnnzmhc_asldkrqrue_fjoxzqwbkits", 24], ["4.2.e_e_ai_ay", "4.16777216.abwmi_bnnzmhc_asldkrqrue_fjoxzqwbkits", 24], ["4.2.e_m_y_bo", "4.16777216.abwmi_bnnzmhc_asldkrqrue_fjoxzqwbkits", 24], ["4.2.g_u_bs_cu", "4.16777216.abwmi_bnnzmhc_asldkrqrue_fjoxzqwbkits", 24], ["4.2.ac_c_a_ae", "4.1073741824.a_nxmrlxw_a_cumskwopkjhrtg", 30], ["4.2.a_a_a_a", "4.281474976710656.alhskyi_cdvourdqednc_agbrknxbmlvuprszme_kshtsekwyvtqduccimlixs", 48], ["4.2.a_ac_a_e", "4.1329227995784915872903807060280344576.adsqyomtlwmkgii_gbeyeldoqpdjlogkezoilesehfc_afqceevzgpohuzkzaekiyhjlmeavsjlqnlofjjooe_dgwdeszvzbhfqgknymdoaslvxjqrgiccnhmjwufnahszqewcqnxjs", 120], ["4.2.a_c_a_e", "4.1329227995784915872903807060280344576.adsqyomtlwmkgii_gbeyeldoqpdjlogkezoilesehfc_afqceevzgpohuzkzaekiyhjlmeavsjlqnlofjjooe_dgwdeszvzbhfqgknymdoaslvxjqrgiccnhmjwufnahszqewcqnxjs", 120]]}