# Stored data for abelian variety isogeny class 4.3.e_i_q_bf, downloaded from the LMFDB on 26 June 2026.
{"abvar_count": 369, "abvar_counts": [369, 6273, 969732, 39350529, 3544437249, 281769208848, 22918638047121, 1714628509573329, 154677606409591236, 12156967554132460833], "abvar_counts_str": "369 6273 969732 39350529 3544437249 281769208848 22918638047121 1714628509573329 154677606409591236 12156967554132460833 ", "angle_corank": 2, "angle_rank": 2, "angles": [0.288152604670988, 0.495448267663691, 0.788152604670988, 0.995448267663691], "center_dim": 8, "cohen_macaulay_max": 1, "curve_count": 8, "curve_counts": [8, 10, 44, 78, 248, 730, 2192, 6054, 20276, 59050], "curve_counts_str": "8 10 44 78 248 730 2192 6054 20276 59050 ", "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": ["8T9"], "geom_dim1_distinct": 0, "geom_dim1_factors": 0, "geom_dim2_distinct": 1, "geom_dim2_factors": 2, "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": 4, "geometric_extension_degree": 4, "geometric_galois_groups": ["4T3"], "geometric_number_fields": ["4.0.4672.2"], "geometric_splitting_field": "4.0.4672.2", "geometric_splitting_polynomials": [[7, -2, 5, -2, 1]], "group_structure_count": 2, "has_geom_ss_factor": false, "has_jacobian": -1, "has_principal_polarization": 1, "hyp_count": 0, "is_cyclic": false, "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.e_i_q_bf", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 24, "newton_coelevation": 6, "newton_elevation": 0, "noncyclic_primes": [3], "number_fields": ["8.0.349241344.2"], "p": 3, "p_rank": 4, "p_rank_deficit": 0, "poly": [1, 4, 8, 16, 31, 48, 72, 108, 81], "poly_str": "1 4 8 16 31 48 72 108 81 ", "primitive_models": [], "q": 3, "real_poly": [1, 4, -4, -20, 1], "simple_distinct": ["4.3.e_i_q_bf"], "simple_factors": ["4.3.e_i_q_bfA"], "simple_multiplicities": [1], "singular_primes": ["3,4*F^3+2*F^2+18*F+9*V^3+15*V^2+2*V+37", "3,2*F^4+3*F^3-6*F^2+5*F+7*V^3+V^2-24*V+8"], "slopes": ["0A", "0B", "0C", "0D", "1A", "1B", "1C", "1D"], "splitting_field": "8.0.349241344.2", "splitting_polynomials": [[17, -52, 96, -100, 81, -40, 18, -4, 1]], "twist_count": 8, "twists": [["4.3.ae_i_aq_bf", "4.9.a_ac_a_aev", 2], ["4.3.ae_o_abg_cp", "4.6561.ato_gwow_abmnuhc_foytjxb", 8], ["4.3.a_ag_a_t", "4.6561.ato_gwow_abmnuhc_foytjxb", 8], ["4.3.a_g_a_t", "4.6561.ato_gwow_abmnuhc_foytjxb", 8], ["4.3.e_o_bg_cp", "4.6561.ato_gwow_abmnuhc_foytjxb", 8], ["4.3.ac_ab_c_e", "4.282429536481.cvqu_aekyemriim_aclhfcplqxsyi_ionbsgxzqgrkmpkwk", 24], ["4.3.c_ab_ac_e", "4.282429536481.cvqu_aekyemriim_aclhfcplqxsyi_ionbsgxzqgrkmpkwk", 24]], "weak_equivalence_count": 4, "zfv_index": 9, "zfv_index_factorization": [[3, 2]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_plus_index": 3, "zfv_plus_index_factorization": [[3, 1]], "zfv_plus_norm": 1, "zfv_singular_count": 4, "zfv_singular_primes": ["3,4*F^3+2*F^2+18*F+9*V^3+15*V^2+2*V+37", "3,2*F^4+3*F^3-6*F^2+5*F+7*V^3+V^2-24*V+8"]}