# Stored data for abelian variety isogeny class 4.3.a_ae_a_h, downloaded from the LMFDB on 20 October 2025.
{"abvar_count": 49, "abvar_counts": [49, 2401, 470596, 39955041, 3500716849, 221460595216, 22857499894369, 1766380438532241, 150103193537593156, 12255018456872488801], "abvar_counts_str": "49 2401 470596 39955041 3500716849 221460595216 22857499894369 1766380438532241 150103193537593156 12255018456872488801 ", "angle_corank": 3, "angle_rank": 1, "angles": [0.0328064302660517, 0.300526903067282, 0.699473096932718, 0.967193569733948], "center_dim": 8, "cohen_macaulay_max": 1, "curve_count": 4, "curve_counts": [4, 2, 28, 78, 244, 554, 2188, 6246, 19684, 59522], "curve_counts_str": "4 2 28 78 244 554 2188 6246 19684 59522 ", "curves": [], "dim1_distinct": 0, "dim1_factors": 0, "dim2_distinct": 0, "dim2_factors": 0, "dim3_distinct": 0, "dim3_factors": 0, "dim4_distinct": 1, "dim4_factors": 1, "dim5_distinct": 0, "dim5_factors": 0, "endomorphism_ring_count": 4, "g": 4, "galois_groups": ["8T3"], "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": 6, "geometric_galois_groups": ["2T1"], "geometric_number_fields": ["2.0.20.1"], "geometric_splitting_field": "2.0.20.1", "geometric_splitting_polynomials": [[5, 0, 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": true, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 0, "label": "4.3.a_ae_a_h", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 120, "newton_coelevation": 6, "newton_elevation": 0, "number_fields": ["8.0.3317760000.3"], "p": 3, "p_rank": 4, "p_rank_deficit": 0, "poly": [1, 0, -4, 0, 7, 0, -36, 0, 81], "poly_str": "1 0 -4 0 7 0 -36 0 81 ", "primitive_models": [], "q": 3, "real_poly": [1, 0, -16, 0, 49], "simple_distinct": ["4.3.a_ae_a_h"], "simple_factors": ["4.3.a_ae_a_hA"], "simple_multiplicities": [1], "singular_primes": ["7,-4*F^3+2*F^2-3*F+3*V^3-7*V", "7,-4*F^4-F+3*V^3+3*V^2-8*V-8"], "slopes": ["0A", "0B", "0C", "0D", "1A", "1B", "1C", "1D"], "splitting_field": "8.0.3317760000.3", "splitting_polynomials": [[81, 0, -36, 0, 7, 0, -4, 0, 1]], "twist_count": 18, "twists": [["4.3.a_i_a_bi", "4.27.a_adk_a_fao", 3], ["4.3.a_e_a_h", "4.81.ae_afu_aq_bddr", 4], ["4.3.ac_c_i_ar", "4.6561.ame_dnju_argvoq_clijbdz", 8], ["4.3.c_c_ai_ar", "4.6561.ame_dnju_argvoq_clijbdz", 8], ["4.3.a_ai_a_bi", "4.531441.acvo_hqypg_alhirnqm_pixkpjela", 12], ["4.3.a_a_a_c", "4.531441.acvo_hqypg_alhirnqm_pixkpjela", 12], ["4.3.a_e_a_h", "4.531441.acvo_hqypg_alhirnqm_pixkpjela", 12], ["4.3.ae_i_au_bu", "4.282429536481.hhxgy_zktordfsm_cbzoykbilqxkea_cyfeducceuxytbndis", 24], ["4.3.ac_ac_c_k", "4.282429536481.hhxgy_zktordfsm_cbzoykbilqxkea_cyfeducceuxytbndis", 24], ["4.3.ac_g_ao_ba", "4.282429536481.hhxgy_zktordfsm_cbzoykbilqxkea_cyfeducceuxytbndis", 24], ["4.3.a_a_a_ac", "4.282429536481.hhxgy_zktordfsm_cbzoykbilqxkea_cyfeducceuxytbndis", 24], ["4.3.c_ac_ac_k", "4.282429536481.hhxgy_zktordfsm_cbzoykbilqxkea_cyfeducceuxytbndis", 24], ["4.3.c_g_o_ba", "4.282429536481.hhxgy_zktordfsm_cbzoykbilqxkea_cyfeducceuxytbndis", 24], ["4.3.e_i_u_bu", "4.282429536481.hhxgy_zktordfsm_cbzoykbilqxkea_cyfeducceuxytbndis", 24], ["4.3.ag_n_ak_b", "4.1797010299914431210413179829509605039731475627537851106401.aqrtrxjhxgywijklkmjirg_esmgbipibifxaxlkbqvihhutapwmbmdzbliuxaoxmy_atwrmkkfmqjrqhfqpadarsubvwcdjnvhvxyuxeknhsbllpyjbjoeddsmesfyiwm_carzufovjfjiqdicoglkaedenxotoghbxjsfiszhhzpqzualhfrvxyvuuckolihiirvvgrqcghcvtrcklvi", 120], ["4.3.ae_n_abe_cj", "4.1797010299914431210413179829509605039731475627537851106401.aqrtrxjhxgywijklkmjirg_esmgbipibifxaxlkbqvihhutapwmbmdzbliuxaoxmy_atwrmkkfmqjrqhfqpadarsubvwcdjnvhvxyuxeknhsbllpyjbjoeddsmesfyiwm_carzufovjfjiqdicoglkaedenxotoghbxjsfiszhhzpqzualhfrvxyvuuckolihiirvvgrqcghcvtrcklvi", 120], ["4.3.e_n_be_cj", "4.1797010299914431210413179829509605039731475627537851106401.aqrtrxjhxgywijklkmjirg_esmgbipibifxaxlkbqvihhutapwmbmdzbliuxaoxmy_atwrmkkfmqjrqhfqpadarsubvwcdjnvhvxyuxeknhsbllpyjbjoeddsmesfyiwm_carzufovjfjiqdicoglkaedenxotoghbxjsfiszhhzpqzualhfrvxyvuuckolihiirvvgrqcghcvtrcklvi", 120], ["4.3.g_n_k_b", "4.1797010299914431210413179829509605039731475627537851106401.aqrtrxjhxgywijklkmjirg_esmgbipibifxaxlkbqvihhutapwmbmdzbliuxaoxmy_atwrmkkfmqjrqhfqpadarsubvwcdjnvhvxyuxeknhsbllpyjbjoeddsmesfyiwm_carzufovjfjiqdicoglkaedenxotoghbxjsfiszhhzpqzualhfrvxyvuuckolihiirvvgrqcghcvtrcklvi", 120]], "weak_equivalence_count": 4, "zfv_index": 49, "zfv_index_factorization": [[7, 2]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_plus_index": 7, "zfv_plus_index_factorization": [[7, 1]], "zfv_plus_norm": 1, "zfv_singular_count": 4, "zfv_singular_primes": ["7,-4*F^3+2*F^2-3*F+3*V^3-7*V", "7,-4*F^4-F+3*V^3+3*V^2-8*V-8"]}