# Stored data for abelian variety isogeny class 5.3.am_cq_ajj_xx_abut, downloaded from the LMFDB on 04 May 2024.
{"label": "5.3.am_cq_ajj_xx_abut", "g": 5, "p": 3, "q": 3, "poly": [1, -12, 68, -243, 621, -1215, 1863, -2187, 1836, -972, 243], "poly_str": "1 -12 68 -243 621 -1215 1863 -2187 1836 -972 243 ", "slopes": ["0A", "0B", "1/2A", "1/2B", "1/2C", "1/2D", "1/2E", "1/2F", "1A", "1B"], "p_rank": 2, "p_rank_deficit": 3, "angles": [0.0975263560045732, 0.166666666666667, 0.166666666666667, 0.166666666666667, 0.527857038681296], "angle_rank": 2, "number_fields": ["2.0.3.1", "4.0.2197.1"], "galois_groups": ["2T1", "4T1"], "center_dim": 6, "abvar_counts": [3, 27783, 12051648, 3723394311, 1242872006928, 278579339071488, 55815405838726341, 12620464084636766631, 3024365235163963572672, 718721523070745713682688], "abvar_counts_str": "3 27783 12051648 3723394311 1242872006928 278579339071488 55815405838726341 12620464084636766631 3024365235163963572672 718721523070745713682688 ", "abvar_count": 3, "curve_counts": [-8, 2, 19, 86, 337, 953, 2428, 6806, 20143, 59117], "curve_counts_str": "-8 2 19 86 337 953 2428 6806 20143 59117 ", "curve_count": -8, "has_jacobian": -1, "has_principal_polarization": 1, "geometric_extension_degree": 6, "geometric_center_dim": 5, "geometric_number_fields": ["1.1.1.1", "4.0.2197.1"], "geometric_galois_groups": ["1T1", "4T1"], "primitive_models": [], "is_primitive": true, "twists": [["5.3.ag_o_aj_abb_dd", "5.9.ai_bi_abb_all_cjh", 2], ["5.3.a_ae_d_j_aj", "5.9.ai_bi_abb_all_cjh", 2], ["5.3.g_o_p_j_j", "5.9.ai_bi_abb_all_cjh", 2], ["5.3.m_cq_jj_xx_but", "5.9.ai_bi_abb_all_cjh", 2], ["5.3.aj_bp_aez_md_axo", "5.27.aj_fw_ablk_mvj_acggc", 3], ["5.3.ag_o_ap_j_aj", "5.27.aj_fw_ablk_mvj_acggc", 3], ["5.3.ag_x_acr_gg_alu", "5.27.aj_fw_ablk_mvj_acggc", 3], ["5.3.ad_f_aj_j_a", "5.27.aj_fw_ablk_mvj_acggc", 3], ["5.3.ad_o_abk_dd_agg", "5.27.aj_fw_ablk_mvj_acggc", 3], ["5.3.a_ae_ad_j_j", "5.27.aj_fw_ablk_mvj_acggc", 3], ["5.3.a_f_ad_a_as", "5.27.aj_fw_ablk_mvj_acggc", 3], ["5.3.d_f_d_aj_abk", "5.27.aj_fw_ablk_mvj_acggc", 3], ["5.3.g_o_j_abb_add", "5.27.aj_fw_ablk_mvj_acggc", 3], ["5.3.ag_u_abz_eh_ahz", "5.81.e_fa_abed_klb_afyfn", 4], ["5.3.a_c_ad_d_aj", "5.81.e_fa_abed_klb_afyfn", 4], ["5.3.a_c_d_d_j", "5.81.e_fa_abed_klb_afyfn", 4], ["5.3.g_u_bz_eh_hz", "5.81.e_fa_abed_klb_afyfn", 4], ["5.3.ad_f_ad_aj_bk", "5.729.ip_bhyk_demcs_fhtzxp_gktovhm", 6], ["5.3.a_f_ad_a_as", "5.729.ip_bhyk_demcs_fhtzxp_gktovhm", 6], ["5.3.a_f_d_a_s", "5.729.ip_bhyk_demcs_fhtzxp_gktovhm", 6], ["5.3.d_f_j_j_a", "5.729.ip_bhyk_demcs_fhtzxp_gktovhm", 6], ["5.3.d_o_bk_dd_gg", "5.729.ip_bhyk_demcs_fhtzxp_gktovhm", 6], ["5.3.g_x_cr_gg_lu", "5.729.ip_bhyk_demcs_fhtzxp_gktovhm", 6], ["5.3.j_bp_ez_md_xo", "5.729.ip_bhyk_demcs_fhtzxp_gktovhm", 6], ["5.3.ad_f_as_bk_abt", "5.19683.rr_iocw_dbccoq_wlelhuj_fcvwsnlpy", 9], ["5.3.ad_f_a_as_bt", "5.19683.rr_iocw_dbccoq_wlelhuj_fcvwsnlpy", 9], ["5.3.ag_l_d_abq_dm", "5.531441.afrx_msqgg_amrzvthq_bzinirrvp_fvsmweirvbi", 12], ["5.3.ad_c_a_ap_cc", "5.531441.afrx_msqgg_amrzvthq_bzinirrvp_fvsmweirvbi", 12], ["5.3.ad_l_abb_cf_aee", "5.531441.afrx_msqgg_amrzvthq_bzinirrvp_fvsmweirvbi", 12], ["5.3.a_ah_ad_m_s", "5.531441.afrx_msqgg_amrzvthq_bzinirrvp_fvsmweirvbi", 12], ["5.3.a_ah_d_m_as", "5.531441.afrx_msqgg_amrzvthq_bzinirrvp_fvsmweirvbi", 12], ["5.3.d_c_a_ap_acc", "5.531441.afrx_msqgg_amrzvthq_bzinirrvp_fvsmweirvbi", 12], ["5.3.d_l_bb_cf_ee", "5.531441.afrx_msqgg_amrzvthq_bzinirrvp_fvsmweirvbi", 12], ["5.3.g_l_ad_abq_adm", "5.531441.afrx_msqgg_amrzvthq_bzinirrvp_fvsmweirvbi", 12], ["5.3.d_f_a_as_abt", "5.387420489.fcop_klpkdqk_mntomyarqs_nmflzbycqafxp_pouvnnwnvmlivebm", 18], ["5.3.d_f_s_bk_bt", "5.387420489.fcop_klpkdqk_mntomyarqs_nmflzbycqafxp_pouvnnwnvmlivebm", 18], ["5.3.ag_r_abh_ci_aee", "5.282429536481.agxxjx_vhbrkuacg_abnxsdrgmwrkabq_cddnmwrkniqwypozfp_acodprftlddtguugrqbabgs", 24], ["5.3.ad_i_as_bh_acc", "5.282429536481.agxxjx_vhbrkuacg_abnxsdrgmwrkabq_cddnmwrkniqwypozfp_acodprftlddtguugrqbabgs", 24], ["5.3.a_ab_ad_g_a", "5.282429536481.agxxjx_vhbrkuacg_abnxsdrgmwrkabq_cddnmwrkniqwypozfp_acodprftlddtguugrqbabgs", 24], ["5.3.a_ab_d_g_a", "5.282429536481.agxxjx_vhbrkuacg_abnxsdrgmwrkabq_cddnmwrkniqwypozfp_acodprftlddtguugrqbabgs", 24], ["5.3.d_i_s_bh_cc", "5.282429536481.agxxjx_vhbrkuacg_abnxsdrgmwrkabq_cddnmwrkniqwypozfp_acodprftlddtguugrqbabgs", 24], ["5.3.g_r_bh_ci_ee", "5.282429536481.agxxjx_vhbrkuacg_abnxsdrgmwrkabq_cddnmwrkniqwypozfp_acodprftlddtguugrqbabgs", 24]], "twist_count": 42, "max_twist_degree": 24, "max_divalg_dim": 1, "max_geom_divalg_dim": 4, "is_simple": false, "is_geometrically_simple": false, "simple_distinct": ["1.3.ad", "2.3.ad_f"], "simple_multiplicities": [3, 1], "simple_factors": ["1.3.adA", "1.3.adB", "1.3.adC", "2.3.ad_fA"], "dim1_factors": 3, "dim2_factors": 1, "dim3_factors": 0, "dim4_factors": 0, "dim5_factors": 0, "dim1_distinct": 1, "dim2_distinct": 1, "dim3_distinct": 0, "dim4_distinct": 0, "dim5_distinct": 0, "geom_dim1_factors": 3, "geom_dim2_factors": 1, "geom_dim3_factors": 0, "geom_dim4_factors": 0, "geom_dim5_factors": 0, "geom_dim1_distinct": 1, "geom_dim2_distinct": 1, "geom_dim3_distinct": 0, "geom_dim4_distinct": 0, "geom_dim5_distinct": 0, "has_geom_ss_factor": true, "real_poly": [1, -12, 53, -99, 54, 27], "geometric_splitting_field": "4.0.2197.1", "splitting_field": "8.0.390971529.1", "geometric_splitting_polynomials": [[3, 4, 2, -1, 1]], "splitting_polynomials": [[9, 12, 10, 14, 5, -10, -1, -1, 1]], "is_squarefree": false, "is_geometrically_squarefree": false}