# Stored data for abelian variety isogeny class 4.2.af_p_abg_bz, downloaded from the LMFDB on 20 October 2025.
{"abvar_count": 2, "abvar_counts": [2, 568, 5894, 32944, 563662, 11717272, 221647232, 4383989856, 78449417018, 1111115335528], "abvar_counts_str": "2 568 5894 32944 563662 11717272 221647232 4383989856 78449417018 1111115335528 ", "angle_corank": 3, "angle_rank": 1, "angles": [0.0435981566527365, 0.329312442367022, 0.384973271918692, 0.527830414775835], "center_dim": 8, "cohen_macaulay_max": 1, "curve_count": -2, "curve_counts": [-2, 10, 13, 6, 13, 43, 103, 262, 580, 1035], "curve_counts_str": "-2 10 13 6 13 43 103 262 580 1035 ", "curves": [], "dim1_distinct": 1, "dim1_factors": 1, "dim2_distinct": 0, "dim2_factors": 0, "dim3_distinct": 1, "dim3_factors": 1, "dim4_distinct": 0, "dim4_factors": 0, "dim5_distinct": 0, "dim5_factors": 0, "endomorphism_ring_count": 1, "g": 4, "galois_groups": ["2T1", "6T1"], "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": 2, "geometric_extension_degree": 14, "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": 0, "is_geometrically_simple": false, "is_geometrically_squarefree": false, "is_primitive": true, "is_simple": false, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 0, "label": "4.2.af_p_abg_bz", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 84, "newton_coelevation": 6, "newton_elevation": 0, "number_fields": ["2.0.7.1", "6.0.16807.1"], "p": 2, "p_rank": 4, "p_rank_deficit": 0, "poly": [1, -5, 15, -32, 51, -64, 60, -40, 16], "poly_str": "1 -5 15 -32 51 -64 60 -40 16 ", "primitive_models": [], "q": 2, "real_poly": [1, -5, 7, -2, -1], "simple_distinct": ["1.2.ab", "3.2.ae_j_ap"], "simple_factors": ["1.2.abA", "3.2.ae_j_apA"], "simple_multiplicities": [1, 1], "singular_primes": [], "slopes": ["0A", "0B", "0C", "0D", "1A", "1B", "1C", "1D"], "splitting_field": "6.0.16807.1", "splitting_polynomials": [[1, -1, 1, -1, 1, -1, 1]], "twist_count": 32, "twists": [["4.2.ad_h_ao_v", "4.4.f_h_ao_acl", 2], ["4.2.d_h_o_v", "4.4.f_h_ao_acl", 2], ["4.2.f_p_bg_bz", "4.4.f_h_ao_acl", 2], ["4.2.c_b_d_j", "4.128.aba_ts_aiha_dzel", 7], ["4.2.c_i_k_x", "4.128.aba_ts_aiha_dzel", 7], ["4.2.ae_h_ah_h", "4.16384.nk_gidi_brfbou_kfqirdp", 14], ["4.2.ae_o_abc_bx", "4.16384.nk_gidi_brfbou_kfqirdp", 14], ["4.2.ac_b_ad_j", "4.16384.nk_gidi_brfbou_kfqirdp", 14], ["4.2.ac_i_ak_x", "4.16384.nk_gidi_brfbou_kfqirdp", 14], ["4.2.a_g_a_r", "4.16384.nk_gidi_brfbou_kfqirdp", 14], ["4.2.e_h_h_h", "4.16384.nk_gidi_brfbou_kfqirdp", 14], ["4.2.e_o_bc_bx", "4.16384.nk_gidi_brfbou_kfqirdp", 14], ["4.2.ab_c_af_f", "4.2097152.iha_sjheu_abbnkmxza_agjwujknnft", 21], ["4.2.ac_c_c_ah", "4.268435456.ftcu_pvayrwg_batfdowxxke_beeylufrsdrsdt", 28], ["4.2.a_ag_a_r", "4.268435456.ftcu_pvayrwg_batfdowxxke_beeylufrsdrsdt", 28], ["4.2.a_a_a_ab", "4.268435456.ftcu_pvayrwg_batfdowxxke_beeylufrsdrsdt", 28], ["4.2.c_c_ac_ah", "4.268435456.ftcu_pvayrwg_batfdowxxke_beeylufrsdrsdt", 28], ["4.2.ad_g_aj_l", "4.4398046511104.abfriqm_rshjnwschy_afxhkxomaoissdcu_bheqqprsroofnyeeffqf", 42], ["4.2.ac_ab_ac_n", "4.4398046511104.abfriqm_rshjnwschy_afxhkxomaoissdcu_bheqqprsroofnyeeffqf", 42], ["4.2.ab_c_f_af", "4.4398046511104.abfriqm_rshjnwschy_afxhkxomaoissdcu_bheqqprsroofnyeeffqf", 42], ["4.2.a_ad_a_f", "4.4398046511104.abfriqm_rshjnwschy_afxhkxomaoissdcu_bheqqprsroofnyeeffqf", 42], ["4.2.b_c_af_af", "4.4398046511104.abfriqm_rshjnwschy_afxhkxomaoissdcu_bheqqprsroofnyeeffqf", 42], ["4.2.b_c_f_f", "4.4398046511104.abfriqm_rshjnwschy_afxhkxomaoissdcu_bheqqprsroofnyeeffqf", 42], ["4.2.c_ab_c_n", "4.4398046511104.abfriqm_rshjnwschy_afxhkxomaoissdcu_bheqqprsroofnyeeffqf", 42], ["4.2.d_g_j_l", "4.4398046511104.abfriqm_rshjnwschy_afxhkxomaoissdcu_bheqqprsroofnyeeffqf", 42], ["4.2.a_a_a_b", "4.72057594037927936.abhawdyy_dqgyuveeomwgs_adaeeruxqlykwnfolfse_eizkqavacbrsrynvkobqexxlp", 56], ["4.2.ab_ab_d_ab", "4.1180591620717411303424.bhuarzlse_tgwmrypmqnrcksru_ghxdbsxpfwnoeqofyjamxuqu_bhqtddcdooolbhkxdjsnenhkkmlttdbt", 70], ["4.2.b_ab_ad_ab", "4.1180591620717411303424.bhuarzlse_tgwmrypmqnrcksru_ghxdbsxpfwnoeqofyjamxuqu_bhqtddcdooolbhkxdjsnenhkkmlttdbt", 70], ["4.2.ab_ae_b_l", "4.19342813113834066795298816.adefkpgvqjs_gjsnnxdnrqvsibinywc_aifewhdheyisrvpsxtakuujxdqnzw_hxfwqhratfprvarkuxiqtyszgqvyxxayhsokf", 84], ["4.2.a_d_a_f", "4.19342813113834066795298816.adefkpgvqjs_gjsnnxdnrqvsibinywc_aifewhdheyisrvpsxtakuujxdqnzw_hxfwqhratfprvarkuxiqtyszgqvyxxayhsokf", 84], ["4.2.b_ae_ab_l", "4.19342813113834066795298816.adefkpgvqjs_gjsnnxdnrqvsibinywc_aifewhdheyisrvpsxtakuujxdqnzw_hxfwqhratfprvarkuxiqtyszgqvyxxayhsokf", 84]], "weak_equivalence_count": 1, "zfv_index": 1, "zfv_index_factorization": [], "zfv_is_bass": true, "zfv_is_maximal": true, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 49, "zfv_singular_count": 0, "zfv_singular_primes": []}