# Stored data for abelian variety isogeny class 3.2.ad_e_ae, downloaded from the LMFDB on 01 February 2026.
{"abvar_count": 2, "abvar_counts": [2, 80, 338, 10400, 57482, 256880, 2525098, 16660800, 124272122, 1161136400], "abvar_counts_str": "2 80 338 10400 57482 256880 2525098 16660800 124272122 1161136400 ", "angle_corank": 1, "angle_rank": 2, "angles": [0.139386741866476, 0.25, 0.686170398078418], "center_dim": 6, "cohen_macaulay_max": 1, "curve_count": 0, "curve_counts": [0, 4, 6, 32, 50, 64, 154, 256, 474, 1104], "curve_counts_str": "0 4 6 32 50 64 154 256 474 1104 ", "curves": ["x^4+x^3*y+x^2*y*z+x^2*z^2+y^4+y^3*z+z^4=0"], "dim1_distinct": 1, "dim1_factors": 1, "dim2_distinct": 1, "dim2_factors": 1, "dim3_distinct": 0, "dim3_factors": 0, "dim4_distinct": 0, "dim4_factors": 0, "dim5_distinct": 0, "dim5_factors": 0, "endomorphism_ring_count": 3, "g": 3, "galois_groups": ["2T1", "4T3"], "geom_dim1_distinct": 1, "geom_dim1_factors": 1, "geom_dim2_distinct": 1, "geom_dim2_factors": 1, "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": 5, "geometric_extension_degree": 4, "geometric_galois_groups": ["1T1", "4T3"], "geometric_number_fields": ["1.1.1.1", "4.0.2312.1"], "geometric_splitting_field": "4.0.1088.2", "geometric_splitting_polynomials": [[2, -4, 5, -2, 1]], "group_structure_count": 1, "has_geom_ss_factor": true, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 0, "is_cyclic": true, "is_geometrically_simple": false, "is_geometrically_squarefree": true, "is_primitive": true, "is_simple": false, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 1, "label": "3.2.ad_e_ae", "max_divalg_dim": 1, "max_geom_divalg_dim": 4, "max_twist_degree": 8, "newton_coelevation": 2, "newton_elevation": 2, "noncyclic_primes": [], "number_fields": ["2.0.4.1", "4.0.2312.1"], "p": 2, "p_rank": 1, "p_rank_deficit": 2, "poly": [1, -3, 4, -4, 8, -12, 8], "poly_str": "1 -3 4 -4 8 -12 8 ", "primitive_models": [], "q": 2, "real_poly": [1, -3, -2, 8], "simple_distinct": ["1.2.ac", "2.2.ab_a"], "simple_factors": ["1.2.acA", "2.2.ab_aA"], "simple_multiplicities": [1, 1], "singular_primes": ["2,F^2-2*V^2+3*V+2,-5*F-2*V^2+4"], "slopes": ["0A", "1/2A", "1/2B", "1/2C", "1/2D", "1A"], "splitting_field": "8.0.18939904.2", "splitting_polynomials": [[2, -12, 30, -44, 43, -28, 14, -4, 1]], "twist_count": 6, "twists": [["3.2.ab_a_e", "3.4.ab_i_ai", 2], ["3.2.b_a_ae", "3.4.ab_i_ai", 2], ["3.2.d_e_e", "3.4.ab_i_ai", 2], ["3.2.ab_c_ae", "3.256.ab_ahk_achc", 8], ["3.2.b_c_e", "3.256.ab_ahk_achc", 8]], "weak_equivalence_count": 3, "zfv_index": 4, "zfv_index_factorization": [[2, 2]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 32, "zfv_singular_count": 3, "zfv_singular_primes": ["2,F^2-2*V^2+3*V+2,-5*F-2*V^2+4"]}