# Stored data for abelian variety isogeny class 4.2.a_a_a_d, downloaded from the LMFDB on 24 September 2025.
{"abvar_count": 20, "abvar_counts": [20, 400, 3980, 160000, 1050500, 15840400, 268421180, 6146560000, 68719312820, 1103550250000], "abvar_counts_str": "20 400 3980 160000 1050500 15840400 268421180 6146560000 68719312820 1103550250000 ", "angle_corank": 3, "angle_rank": 1, "angles": [0.155589323384781, 0.344410676615219, 0.655589323384781, 0.844410676615219], "center_dim": 8, "cohen_macaulay_max": 1, "curve_count": 3, "curve_counts": [3, 5, 9, 29, 33, 65, 129, 349, 513, 1025], "curve_counts_str": "3 5 9 29 33 65 129 349 513 1025 ", "curves": ["y^2 + (x^4 + x + 1)*y=x^9 + x^3 + x^2 + 1", "y^2 + (x^4 + x + 1)*y=x^9 + x^3 + x^2"], "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": 9, "g": 4, "galois_groups": ["8T9"], "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": 4, "geometric_galois_groups": ["2T1"], "geometric_number_fields": ["2.0.55.1"], "geometric_splitting_field": "2.0.55.1", "geometric_splitting_polynomials": [[14, -1, 1]], "group_structure_count": 2, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 2, "is_geometrically_simple": false, "is_geometrically_squarefree": false, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 5, "label": "4.2.a_a_a_d", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 8, "newton_coelevation": 6, "newton_elevation": 0, "number_fields": ["8.0.2342560000.5"], "p": 2, "p_rank": 4, "p_rank_deficit": 0, "poly": [1, 0, 0, 0, 3, 0, 0, 0, 16], "poly_str": "1 0 0 0 3 0 0 0 16 ", "primitive_models": [], "q": 2, "real_poly": [1, 0, -8, 0, 11], "simple_distinct": ["4.2.a_a_a_d"], "simple_factors": ["4.2.a_a_a_dA"], "simple_multiplicities": [1], "singular_primes": ["2,3*F^3-F+5*V+1", "2,4*F^3+3*F^2+F+7*V+2"], "slopes": ["0A", "0B", "0C", "0D", "1A", "1B", "1C", "1D"], "splitting_field": "8.0.309760000.3", "splitting_polynomials": [[1, 6, 18, -2, -1, -2, 8, -4, 1]], "twist_count": 2, "twists": [["4.2.a_a_a_ad", "4.256.do_gfm_gunk_fatqf", 8]], "weak_equivalence_count": 9, "zfv_index": 16, "zfv_index_factorization": [[2, 4]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_plus_index": 4, "zfv_plus_index_factorization": [[2, 2]], "zfv_plus_norm": 121, "zfv_singular_count": 4, "zfv_singular_primes": ["2,3*F^3-F+5*V+1", "2,4*F^3+3*F^2+F+7*V+2"]}