# Stored data for abelian variety isogeny class 2.7.a_ae, downloaded from the LMFDB on 07 March 2026.
{"abvar_count": 46, "abvar_counts": [46, 2116, 118174, 6170256, 282441886, 13965094276, 678224550574, 33210785894400, 1628413556844046, 79773418967236996], "abvar_counts_str": "46 2116 118174 6170256 282441886 13965094276 678224550574 33210785894400 1628413556844046 79773418967236996 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 1, "angle_rank": 1, "angles": [0.203884584447166, 0.796115415552834], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 8, "curve_counts": [8, 42, 344, 2566, 16808, 118698, 823544, 5760958, 40353608, 282408522], "curve_counts_str": "8 42 344 2566 16808 118698 823544 5760958 40353608 282408522 ", "curves": ["y^2=x^6+4*x^5+2*x^4+6*x^2+6*x+6", "y^2=2*x^5+x^4+6*x^2+6*x+3", "y^2=6*x^5+3*x^4+4*x^2+4*x+2"], "dim1_distinct": 0, "dim1_factors": 0, "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": 2, "g": 2, "galois_groups": ["4T2"], "geom_dim1_distinct": 1, "geom_dim1_factors": 2, "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": 2, "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": 3, "is_cyclic": true, "is_geometrically_simple": false, "is_geometrically_squarefree": false, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 3, "label": "2.7.a_ae", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 8, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [], "number_fields": ["4.0.6400.2"], "p": 7, "p_rank": 2, "p_rank_deficit": 0, "pic_prime_gens": [[1, 2, 1, 2], [1, 7, 1, 2]], "poly": [1, 0, -4, 0, 49], "poly_str": "1 0 -4 0 49 ", "primitive_models": [], "principal_polarization_count": 6, "q": 7, "real_poly": [1, 0, -18], "simple_distinct": ["2.7.a_ae"], "simple_factors": ["2.7.a_aeA"], "simple_multiplicities": [1], "singular_primes": ["3,-F-4*V-6"], "size": 6, "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.6400.2", "splitting_polynomials": [[9, 0, 4, 0, 1]], "twist_count": 4, "twists": [["2.7.a_e", "2.2401.gi_rbi", 4], ["2.7.ag_s", "2.5764801.afrw_bhiegk", 8], ["2.7.g_s", "2.5764801.afrw_bhiegk", 8]], "weak_equivalence_count": 2, "zfv_index": 9, "zfv_index_factorization": [[3, 2]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_pic_size": 4, "zfv_plus_index": 3, "zfv_plus_index_factorization": [[3, 1]], "zfv_plus_norm": 100, "zfv_singular_count": 2, "zfv_singular_primes": ["3,-F-4*V-6"]}