# Stored data for abelian variety isogeny class 4.2.a_a_ac_a, downloaded from the LMFDB on 17 January 2026.
{"abvar_count": 11, "abvar_counts": [11, 253, 1727, 74129, 537581, 13862629, 272117857, 5535434817, 65832284969, 1017475795633], "abvar_counts_str": "11 253 1727 74129 537581 13862629 272117857 5535434817 65832284969 1017475795633 ", "angle_corank": 0, "angle_rank": 4, "angles": [0.0640918585256743, 0.393625989811032, 0.651207033805291, 0.823657974581194], "center_dim": 8, "cohen_macaulay_max": 2, "curve_count": 3, "curve_counts": [3, 5, 3, 17, 13, 53, 129, 321, 489, 945], "curve_counts_str": "3 5 3 17 13 53 129 321 489 945 ", "curves": ["y^2 + y=x^9 + x^7 + x^3 + 1"], "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": 6, "g": 4, "galois_groups": ["8T44"], "geom_dim1_distinct": 0, "geom_dim1_factors": 0, "geom_dim2_distinct": 0, "geom_dim2_factors": 0, "geom_dim3_distinct": 0, "geom_dim3_factors": 0, "geom_dim4_distinct": 1, "geom_dim4_factors": 1, "geom_dim5_distinct": 0, "geom_dim5_factors": 0, "geometric_center_dim": 8, "geometric_extension_degree": 1, "geometric_galois_groups": ["8T44"], "geometric_number_fields": ["8.0.5198736512.1"], "geometric_splitting_field": "8.0.5198736512.1", "geometric_splitting_polynomials": [[16, -24, 12, -2, 0, -1, 3, -3, 1]], "group_structure_count": 1, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 1, "is_cyclic": true, "is_geometrically_simple": true, "is_geometrically_squarefree": true, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 1, "label": "4.2.a_a_ac_a", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 2, "newton_coelevation": 1, "newton_elevation": 5, "noncyclic_primes": [], "number_fields": ["8.0.5198736512.1"], "p": 2, "p_rank": 0, "p_rank_deficit": 4, "poly": [1, 0, 0, -2, 0, -4, 0, 0, 16], "poly_str": "1 0 0 -2 0 -4 0 0 16 ", "primitive_models": [], "q": 2, "real_poly": [1, 0, -8, -2, 8], "simple_distinct": ["4.2.a_a_ac_a"], "simple_factors": ["4.2.a_a_ac_aA"], "simple_multiplicities": [1], "singular_primes": ["2,-2*F^3-F+4*V^2+2*V-4,2*F^4-2*F^2-V^3-3*V-2"], "slopes": ["1/3A", "1/3B", "1/3C", "1/2A", "1/2B", "2/3A", "2/3B", "2/3C"], "splitting_field": "8.0.5198736512.1", "splitting_polynomials": [[16, -24, 12, -2, 0, -1, 3, -3, 1]], "twist_count": 2, "twists": [["4.2.a_a_c_a", "4.4.a_a_ae_q", 2]], "weak_equivalence_count": 7, "zfv_index": 8, "zfv_index_factorization": [[2, 3]], "zfv_is_bass": false, "zfv_is_maximal": false, "zfv_plus_index": 2, "zfv_plus_index_factorization": [[2, 1]], "zfv_plus_norm": 32, "zfv_singular_count": 3, "zfv_singular_primes": ["2,-2*F^3-F+4*V^2+2*V-4,2*F^4-2*F^2-V^3-3*V-2"]}