# Stored data for abelian variety isogeny class 1.9.ae, downloaded from the LMFDB on 14 October 2025.
{"abvar_count": 6, "abvar_counts": [6, 84, 774, 6720, 59286, 530964, 4778934, 43034880, 387409446, 3486846804], "abvar_counts_str": "6 84 774 6720 59286 530964 4778934 43034880 387409446 3486846804 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 0, "angle_rank": 1, "angles": [0.26772047280123], "center_dim": 2, "cohen_macaulay_max": 1, "curve_count": 6, "curve_counts": [6, 84, 774, 6720, 59286, 530964, 4778934, 43034880, 387409446, 3486846804], "curve_counts_str": "6 84 774 6720 59286 530964 4778934 43034880 387409446 3486846804 ", "curves": ["y^2+x*y=x^3+a", "y^2+x*y=x^3+a^3"], "dim1_distinct": 1, "dim1_factors": 1, "dim2_distinct": 0, "dim2_factors": 0, "dim3_distinct": 0, "dim3_factors": 0, "dim4_distinct": 0, "dim4_factors": 0, "dim5_distinct": 0, "dim5_factors": 0, "endomorphism_ring_count": 1, "g": 1, "galois_groups": ["2T1"], "geom_dim1_distinct": 1, "geom_dim1_factors": 1, "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": 1, "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": 0, "is_geometrically_simple": true, "is_geometrically_squarefree": true, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 2, "label": "1.9.ae", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 2, "newton_coelevation": 1, "newton_elevation": 0, "number_fields": ["2.0.20.1"], "p": 3, "p_rank": 1, "p_rank_deficit": 0, "poly": [1, -4, 9], "poly_str": "1 -4 9 ", "primitive_models": [], "principal_polarization_count": 2, "q": 9, "real_poly": [1, -4], "simple_distinct": ["1.9.ae"], "simple_factors": ["1.9.aeA"], "simple_multiplicities": [1], "singular_primes": [], "size": 2, "slopes": ["0A", "1A"], "splitting_field": "2.0.20.1", "splitting_polynomials": [[5, 0, 1]], "twist_count": 2, "twists": [["1.9.e", "1.81.c", 2]], "weak_equivalence_count": 1, "zfv_index": 1, "zfv_index_factorization": [], "zfv_is_bass": true, "zfv_is_maximal": true, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 20, "zfv_singular_count": 0, "zfv_singular_primes": []}