# Stored data for abelian variety isogeny class 4.5.a_q_a_ek, downloaded from the LMFDB on 16 April 2026.
{"abvar_count": 1156, "abvar_counts": [1156, 1336336, 241429444, 140283207936, 95245771247236, 58288176430149136, 37252509345522290884, 23535616807151861760000, 14551941500420030499395716, 9071756940480807939037639696], "abvar_counts_str": "1156 1336336 241429444 140283207936 95245771247236 58288176430149136 37252509345522290884 23535616807151861760000 14551941500420030499395716 9071756940480807939037639696 ", "angle_corank": 3, "angle_rank": 1, "angles": [0.397583617650433, 0.397583617650433, 0.602416382349567, 0.602416382349567], "center_dim": 4, "curve_count": 6, "curve_counts": [6, 58, 126, 570, 3126, 15274, 78126, 394842, 1953126, 9740698], "curve_counts_str": "6 58 126 570 3126 15274 78126 394842 1953126 9740698 ", "curves": [], "dim1_distinct": 0, "dim1_factors": 0, "dim2_distinct": 1, "dim2_factors": 2, "dim3_distinct": 0, "dim3_factors": 0, "dim4_distinct": 0, "dim4_factors": 0, "dim5_distinct": 0, "dim5_factors": 0, "g": 4, "galois_groups": ["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": 2, "geometric_extension_degree": 2, "geometric_galois_groups": ["2T1"], "geometric_number_fields": ["2.0.4.1"], "geometric_splitting_field": "2.0.4.1", "geometric_splitting_polynomials": [[1, 0, 1]], "has_geom_ss_factor": false, "has_jacobian": 0, "has_principal_polarization": 1, "hyp_count": 0, "is_cyclic": false, "is_geometrically_simple": false, "is_geometrically_squarefree": false, "is_primitive": true, "is_simple": false, "is_squarefree": false, "is_supersingular": false, "label": "4.5.a_q_a_ek", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 40, "newton_coelevation": 6, "newton_elevation": 0, "noncyclic_primes": [2, 17], "number_fields": ["4.0.256.1"], "p": 5, "p_rank": 4, "p_rank_deficit": 0, "poly": [1, 0, 16, 0, 114, 0, 400, 0, 625], "poly_str": "1 0 16 0 114 0 400 0 625 ", "primitive_models": [], "q": 5, "real_poly": [1, 0, -4, 0, 4], "simple_distinct": ["2.5.a_i"], "simple_factors": ["2.5.a_iA", "2.5.a_iB"], "simple_multiplicities": [2], "slopes": ["0A", "0B", "0C", "0D", "1A", "1B", "1C", "1D"], "splitting_field": "4.0.256.1", "splitting_polynomials": [[1, 0, 0, 0, 1]], "twist_count": 124, "twists": [["4.5.a_ai_a_bn", "4.125.a_agu_a_cfru", 3], ["4.5.a_aq_a_ek", "4.625.ace_flk_agpoq_ilemg", 4], ["4.5.a_a_a_ao", "4.625.ace_flk_agpoq_ilemg", 4], ["4.5.aq_em_atc_cao", "4.390625.gge_sadpk_bfeasxoq_bjfzvduxsg", 8], ["4.5.ao_do_aog_bmk", "4.390625.gge_sadpk_bfeasxoq_bjfzvduxsg", 8], ["4.5.am_cu_akq_bcg", "4.390625.gge_sadpk_bfeasxoq_bjfzvduxsg", 8], ["4.5.ak_bs_aeo_kc", "4.390625.gge_sadpk_bfeasxoq_bjfzvduxsg", 8], ["4.5.ak_ce_ahy_uw", "4.390625.gge_sadpk_bfeasxoq_bjfzvduxsg", 8], ["4.5.ai_s_y_agc", "4.390625.gge_sadpk_bfeasxoq_bjfzvduxsg", 8], ["4.5.ai_u_i_aec", "4.390625.gge_sadpk_bfeasxoq_bjfzvduxsg", 8], ["4.5.ai_bg_adk_hy", "4.390625.gge_sadpk_bfeasxoq_bjfzvduxsg", 8], ["4.5.ai_bi_aea_jy", "4.390625.gge_sadpk_bfeasxoq_bjfzvduxsg", 8], ["4.5.ai_bs_afw_pq", "4.390625.gge_sadpk_bfeasxoq_bjfzvduxsg", 8], ["4.5.ag_k_s_adq", "4.390625.gge_sadpk_bfeasxoq_bjfzvduxsg", 8], ["4.5.ag_m_g_acg", "4.390625.gge_sadpk_bfeasxoq_bjfzvduxsg", 8], ["4.5.ag_y_aco_gc", "4.390625.gge_sadpk_bfeasxoq_bjfzvduxsg", 8], ["4.5.ag_ba_ada_hm", "4.390625.gge_sadpk_bfeasxoq_bjfzvduxsg", 8], ["4.5.ae_g_m_ack", "4.390625.gge_sadpk_bfeasxoq_bjfzvduxsg", 8], ["4.5.ae_i_abc_dq", "4.390625.gge_sadpk_bfeasxoq_bjfzvduxsg", 8], ["4.5.ae_i_e_abi", "4.390625.gge_sadpk_bfeasxoq_bjfzvduxsg", 8], ["4.5.ae_u_abs_fe", "4.390625.gge_sadpk_bfeasxoq_bjfzvduxsg", 8], ["4.5.ae_w_aca_gg", "4.390625.gge_sadpk_bfeasxoq_bjfzvduxsg", 8], ["4.5.ac_ag_g_bi", "4.390625.gge_sadpk_bfeasxoq_bjfzvduxsg", 8], ["4.5.ac_ae_c_bm", "4.390625.gge_sadpk_bfeasxoq_bjfzvduxsg", 8], ["4.5.ac_i_aw_ck", "4.390625.gge_sadpk_bfeasxoq_bjfzvduxsg", 8], ["4.5.ac_i_k_ac", "4.390625.gge_sadpk_bfeasxoq_bjfzvduxsg", 8], ["4.5.ac_k_aba_co", "4.390625.gge_sadpk_bfeasxoq_bjfzvduxsg", 8], ["4.5.a_ao_a_du", "4.390625.gge_sadpk_bfeasxoq_bjfzvduxsg", 8], ["4.5.a_am_a_di", "4.390625.gge_sadpk_bfeasxoq_bjfzvduxsg", 8], ["4.5.a_ac_a_c", "4.390625.gge_sadpk_bfeasxoq_bjfzvduxsg", 8], ["4.5.a_a_a_o", "4.390625.gge_sadpk_bfeasxoq_bjfzvduxsg", 8], ["4.5.a_c_a_c", "4.390625.gge_sadpk_bfeasxoq_bjfzvduxsg", 8], ["4.5.a_m_a_di", "4.390625.gge_sadpk_bfeasxoq_bjfzvduxsg", 8], ["4.5.a_o_a_du", "4.390625.gge_sadpk_bfeasxoq_bjfzvduxsg", 8], ["4.5.c_ag_ag_bi", "4.390625.gge_sadpk_bfeasxoq_bjfzvduxsg", 8], ["4.5.c_ae_ac_bm", "4.390625.gge_sadpk_bfeasxoq_bjfzvduxsg", 8], ["4.5.c_i_ak_ac", "4.390625.gge_sadpk_bfeasxoq_bjfzvduxsg", 8], ["4.5.c_i_w_ck", "4.390625.gge_sadpk_bfeasxoq_bjfzvduxsg", 8], ["4.5.c_k_ba_co", "4.390625.gge_sadpk_bfeasxoq_bjfzvduxsg", 8], ["4.5.e_g_am_ack", "4.390625.gge_sadpk_bfeasxoq_bjfzvduxsg", 8], ["4.5.e_i_ae_abi", "4.390625.gge_sadpk_bfeasxoq_bjfzvduxsg", 8], ["4.5.e_i_bc_dq", "4.390625.gge_sadpk_bfeasxoq_bjfzvduxsg", 8], ["4.5.e_u_bs_fe", "4.390625.gge_sadpk_bfeasxoq_bjfzvduxsg", 8], ["4.5.e_w_ca_gg", "4.390625.gge_sadpk_bfeasxoq_bjfzvduxsg", 8], ["4.5.g_k_as_adq", "4.390625.gge_sadpk_bfeasxoq_bjfzvduxsg", 8], ["4.5.g_m_ag_acg", "4.390625.gge_sadpk_bfeasxoq_bjfzvduxsg", 8], ["4.5.g_y_co_gc", "4.390625.gge_sadpk_bfeasxoq_bjfzvduxsg", 8], ["4.5.g_ba_da_hm", "4.390625.gge_sadpk_bfeasxoq_bjfzvduxsg", 8], ["4.5.i_s_ay_agc", "4.390625.gge_sadpk_bfeasxoq_bjfzvduxsg", 8], ["4.5.i_u_ai_aec", "4.390625.gge_sadpk_bfeasxoq_bjfzvduxsg", 8], ["4.5.i_bg_dk_hy", "4.390625.gge_sadpk_bfeasxoq_bjfzvduxsg", 8], ["4.5.i_bi_ea_jy", "4.390625.gge_sadpk_bfeasxoq_bjfzvduxsg", 8], ["4.5.i_bs_fw_pq", "4.390625.gge_sadpk_bfeasxoq_bjfzvduxsg", 8], ["4.5.k_bs_eo_kc", "4.390625.gge_sadpk_bfeasxoq_bjfzvduxsg", 8], ["4.5.k_ce_hy_uw", "4.390625.gge_sadpk_bfeasxoq_bjfzvduxsg", 8], ["4.5.m_cu_kq_bcg", "4.390625.gge_sadpk_bfeasxoq_bjfzvduxsg", 8], ["4.5.o_do_og_bmk", "4.390625.gge_sadpk_bfeasxoq_bjfzvduxsg", 8], ["4.5.q_em_tc_cao", "4.390625.gge_sadpk_bfeasxoq_bjfzvduxsg", 8], ["4.5.a_i_a_bn", "4.244140625.fjci_nxfqrpc_wgognvrsse_xxqwroxdazrus", 12], ["4.5.a_a_a_abw", "4.152587890625.acxarw_gbeqvbwfk_ahvngdrgbxixvk_iazkgasgglosronog", 16], ["4.5.a_a_a_bw", "4.152587890625.acxarw_gbeqvbwfk_ahvngdrgbxixvk_iazkgasgglosronog", 16], ["4.5.am_cr_ajs_zg", "4.59604644775390625.avqkkei_ctsjplyjhprdc_abpmdwhlnwghdwsultie_criugzvnvxyervexblrlefnms", 24], ["4.5.ak_bp_adq_hc", "4.59604644775390625.avqkkei_ctsjplyjhprdc_abpmdwhlnwghdwsultie_criugzvnvxyervexblrlefnms", 24], ["4.5.ak_cb_ahg_su", "4.59604644775390625.avqkkei_ctsjplyjhprdc_abpmdwhlnwghdwsultie_criugzvnvxyervexblrlefnms", 24], ["4.5.ai_bd_acs_fw", "4.59604644775390625.avqkkei_ctsjplyjhprdc_abpmdwhlnwghdwsultie_criugzvnvxyervexblrlefnms", 24], ["4.5.ai_bm_aey_mt", "4.59604644775390625.avqkkei_ctsjplyjhprdc_abpmdwhlnwghdwsultie_criugzvnvxyervexblrlefnms", 24], ["4.5.ai_bp_afk_oa", "4.59604644775390625.avqkkei_ctsjplyjhprdc_abpmdwhlnwghdwsultie_criugzvnvxyervexblrlefnms", 24], ["4.5.ag_j_be_afg", "4.59604644775390625.avqkkei_ctsjplyjhprdc_abpmdwhlnwghdwsultie_criugzvnvxyervexblrlefnms", 24], ["4.5.ag_s_abw_ep", "4.59604644775390625.avqkkei_ctsjplyjhprdc_abpmdwhlnwghdwsultie_criugzvnvxyervexblrlefnms", 24], ["4.5.ag_v_aci_fw", "4.59604644775390625.avqkkei_ctsjplyjhprdc_abpmdwhlnwghdwsultie_criugzvnvxyervexblrlefnms", 24], ["4.5.ag_v_acc_em", "4.59604644775390625.avqkkei_ctsjplyjhprdc_abpmdwhlnwghdwsultie_criugzvnvxyervexblrlefnms", 24], ["4.5.ae_c_aq_dn", "4.59604644775390625.avqkkei_ctsjplyjhprdc_abpmdwhlnwghdwsultie_criugzvnvxyervexblrlefnms", 24], ["4.5.ae_d_m_abm", "4.59604644775390625.avqkkei_ctsjplyjhprdc_abpmdwhlnwghdwsultie_criugzvnvxyervexblrlefnms", 24], ["4.5.ae_f_aw_dk", 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