# Stored data for abelian variety isogeny class 3.4.af_k_aq, downloaded from the LMFDB on 16 May 2024.
{"label": "3.4.af_k_aq", "g": 3, "p": 2, "q": 4, "poly": [1, -5, 10, -16, 40, -80, 64], "poly_str": "1 -5 10 -16 40 -80 64 ", "slopes": ["0A", "1/2A", "1/2B", "1/2C", "1/2D", "1A"], "p_rank": 1, "p_rank_deficit": 2, "angles": [0.0, 0.0, 0.230053456162616, 0.666666666666667], "angle_rank": 1, "number_fields": ["1.1.1.1", "2.0.7.1", "2.0.3.1"], "galois_groups": ["1T1", "2T1", "2T1"], "center_dim": 5, "abvar_counts": [14, 3024, 177674, 17690400, 1099070714, 65280270384, 4340779608746, 278458819329600, 17806024993090586, 1150477478165396304], "abvar_counts_str": "14 3024 177674 17690400 1099070714 65280270384 4340779608746 278458819329600 17806024993090586 1150477478165396304 ", "abvar_count": 14, "curve_counts": [0, 12, 42, 272, 1050, 3888, 16170, 64832, 259098, 1046352], "curve_counts_str": "0 12 42 272 1050 3888 16170 64832 259098 1046352 ", "curve_count": 0, "has_jacobian": 0, "has_principal_polarization": 1, "geometric_extension_degree": 3, "geometric_center_dim": 3, "geometric_number_fields": ["1.1.1.1", "2.0.7.1"], "geometric_galois_groups": ["1T1", "2T1"], "primitive_models": [], "is_primitive": true, "twists": [["3.4.aj_bm_ads", "3.16.af_u_aey", 2], ["3.4.ad_c_a", "3.16.af_u_aey", 2], ["3.4.ab_ac_q", "3.16.af_u_aey", 2], ["3.4.b_ac_aq", "3.16.af_u_aey", 2], ["3.4.d_c_a", "3.16.af_u_aey", 2], ["3.4.f_k_q", "3.16.af_u_aey", 2], ["3.4.j_bm_ds", "3.16.af_u_aey", 2], ["3.4.al_ca_afg", "3.64.ax_ge_ayq", 3], ["3.4.b_e_ae", "3.64.ax_ge_ayq", 3], ["3.4.af_s_abo", "3.256.p_ajg_amdc", 4], ["3.4.ab_g_ai", "3.256.p_ajg_amdc", 4], ["3.4.b_g_i", "3.256.p_ajg_amdc", 4], ["3.4.f_s_bo", "3.256.p_ajg_amdc", 4], ["3.4.ah_bc_acq", "3.4096.aib_yqa_acbppw", 6], ["3.4.af_e_i", "3.4096.aib_yqa_acbppw", 6], ["3.4.ad_ae_y", "3.4096.aib_yqa_acbppw", 6], ["3.4.ad_i_am", "3.4096.aib_yqa_acbppw", 6], ["3.4.ab_e_e", "3.4096.aib_yqa_acbppw", 6], ["3.4.d_ae_ay", "3.4096.aib_yqa_acbppw", 6], ["3.4.d_i_m", "3.4096.aib_yqa_acbppw", 6], ["3.4.f_e_ai", "3.4096.aib_yqa_acbppw", 6], ["3.4.h_bc_cq", "3.4096.aib_yqa_acbppw", 6], ["3.4.l_ca_fg", "3.4096.aib_yqa_acbppw", 6], ["3.4.ah_y_ace", "3.16777216.apkb_bqmqmi_gnztlohk", 12], ["3.4.ad_a_m", "3.16777216.apkb_bqmqmi_gnztlohk", 12], ["3.4.ad_m_ay", "3.16777216.apkb_bqmqmi_gnztlohk", 12], ["3.4.ab_a_ai", "3.16777216.apkb_bqmqmi_gnztlohk", 12], ["3.4.b_a_i", "3.16777216.apkb_bqmqmi_gnztlohk", 12], ["3.4.d_a_am", "3.16777216.apkb_bqmqmi_gnztlohk", 12], ["3.4.d_m_y", "3.16777216.apkb_bqmqmi_gnztlohk", 12], ["3.4.h_y_ce", "3.16777216.apkb_bqmqmi_gnztlohk", 12], ["3.4.ab_c_e", "3.1073741824.agwzf_ubhxkya_abnwqmcxapqu", 15], ["3.4.ad_e_a", "3.281474976710656.afvttvl_papqthymwnw_ayuiipchyhbqowbcy", 24], ["3.4.d_e_a", "3.281474976710656.afvttvl_papqthymwnw_ayuiipchyhbqowbcy", 24], ["3.4.af_o_abc", "3.1152921504606846976.ahhicauz_ahnafgrcpihsts_fochkbpabxtkpyrnaeyq", 30], ["3.4.b_c_ae", "3.1152921504606846976.ahhicauz_ahnafgrcpihsts_fochkbpabxtkpyrnaeyq", 30], ["3.4.f_o_bc", "3.1152921504606846976.ahhicauz_ahnafgrcpihsts_fochkbpabxtkpyrnaeyq", 30]], "twist_count": 38, "max_twist_degree": 30, "max_divalg_dim": 4, "max_geom_divalg_dim": 4, "is_simple": false, "is_geometrically_simple": false, "simple_distinct": ["1.4.ae", "1.4.ad", "1.4.c"], "simple_multiplicities": [1, 1, 1], "simple_factors": ["1.4.aeA", "1.4.adA", "1.4.cA"], "dim1_factors": 3, "dim2_factors": 0, "dim3_factors": 0, "dim4_factors": 0, "dim5_factors": 0, "dim1_distinct": 3, "dim2_distinct": 0, "dim3_distinct": 0, "dim4_distinct": 0, "dim5_distinct": 0, "geom_dim1_factors": 3, "geom_dim2_factors": 0, "geom_dim3_factors": 0, "geom_dim4_factors": 0, "geom_dim5_factors": 0, "geom_dim1_distinct": 2, "geom_dim2_distinct": 0, "geom_dim3_distinct": 0, "geom_dim4_distinct": 0, "geom_dim5_distinct": 0, "has_geom_ss_factor": true, "real_poly": [1, -5, -2, 24], "curves": [], "geometric_splitting_field": "2.0.7.1", "splitting_field": "4.0.441.1", "geometric_splitting_polynomials": [[2, -1, 1]], "splitting_polynomials": [[4, -2, -1, -1, 1]], "is_squarefree": true, "is_geometrically_squarefree": false}