# Stored data for abelian variety isogeny class 1.67.ae, downloaded from the LMFDB on 01 September 2025.
{"abvar_count": 64, "abvar_counts": [64, 4608, 301504, 20146176, 1350055744, 90458436096, 6060716468416, 406067693395968, 27206534133825088, 1822837802440647168], "abvar_counts_str": "64 4608 301504 20146176 1350055744 90458436096 6060716468416 406067693395968 27206534133825088 1822837802440647168 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 0, "angle_rank": 1, "angles": [0.421429069537878], "center_dim": 2, "cohen_macaulay_max": 1, "curve_count": 64, "curve_counts": [64, 4608, 301504, 20146176, 1350055744, 90458436096, 6060716468416, 406067693395968, 27206534133825088, 1822837802440647168], "curve_counts_str": "64 4608 301504 20146176 1350055744 90458436096 6060716468416 406067693395968 27206534133825088 1822837802440647168 ", "curves": ["y^2=x^3+61*x+55", "y^2=x^3+52*x+37", "y^2=x^3+14*x+14", "y^2=x^3+30*x+60", "y^2=x^3+42*x+42", "y^2=x^3+22*x+44", "y^2=x^3+19*x+38", "y^2=x^3+5*x+5", "y^2=x^3+17*x+17", "y^2=x^3+33*x+33"], "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": 4, "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": ["2.0.7.1"], "geometric_splitting_field": "2.0.7.1", "geometric_splitting_polynomials": [[2, -1, 1]], "group_structure_count": 2, "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": 10, "label": "1.67.ae", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 2, "newton_coelevation": 1, "newton_elevation": 0, "number_fields": ["2.0.7.1"], "p": 67, "p_rank": 1, "p_rank_deficit": 0, "poly": [1, -4, 67], "poly_str": "1 -4 67 ", "primitive_models": [], "principal_polarization_count": 10, "q": 67, "real_poly": [1, -4], "simple_distinct": ["1.67.ae"], "simple_factors": ["1.67.aeA"], "simple_multiplicities": [1], "singular_primes": ["2,F+1", "3,-F-1"], "size": 10, "slopes": ["0A", "1A"], "splitting_field": "2.0.7.1", "splitting_polynomials": [[2, -1, 1]], "twist_count": 2, "twists": [["1.67.e", "1.4489.eo", 2]], "weak_equivalence_count": 4, "zfv_index": 6, "zfv_index_factorization": [[2, 1], [3, 1]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 252, "zfv_singular_count": 4, "zfv_singular_primes": ["2,F+1", "3,-F-1"]}