# Stored data for abelian variety isogeny class 1.67.f, downloaded from the LMFDB on 16 March 2026.
{"abvar_count": 73, "abvar_counts": [73, 4599, 299884, 20148219, 1350198583, 90458209296, 6060707546869, 406067709431475, 27206534508837268, 1822837801853436039], "abvar_counts_str": "73 4599 299884 20148219 1350198583 90458209296 6060707546869 406067709431475 27206534508837268 1822837801853436039 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 0, "angle_rank": 1, "angles": [0.598798062001515], "center_dim": 2, "cohen_macaulay_max": 1, "curve_count": 73, "curve_counts": [73, 4599, 299884, 20148219, 1350198583, 90458209296, 6060707546869, 406067709431475, 27206534508837268, 1822837801853436039], "curve_counts_str": "73 4599 299884 20148219 1350198583 90458209296 6060707546869 406067709431475 27206534508837268 1822837801853436039 ", "curves": ["y^2=x^3+2", "y^2=x^3+42*x+17", "y^2=x^3+30*x+30", "y^2=x^3+23*x+23", "y^2=x^3+51*x+35"], "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": 3, "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": ["2.0.3.1"], "geometric_splitting_field": "2.0.3.1", "geometric_splitting_polynomials": [[1, -1, 1]], "group_structure_count": 1, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 0, "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": 5, "label": "1.67.f", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 6, "newton_coelevation": 1, "newton_elevation": 0, "noncyclic_primes": [], "number_fields": ["2.0.3.1"], "p": 67, "p_rank": 1, "p_rank_deficit": 0, "pic_prime_gens": [[1, 7, 1, 3]], "poly": [1, 5, 67], "poly_str": "1 5 67 ", "primitive_models": [], "principal_polarization_count": 5, "q": 67, "real_poly": [1, 5], "simple_distinct": ["1.67.f"], "simple_factors": ["1.67.fA"], "simple_multiplicities": [1], "singular_primes": ["3,-F-1"], "size": 5, "slopes": ["0A", "1A"], "splitting_field": "2.0.3.1", "splitting_polynomials": [[1, -1, 1]], "twist_count": 6, "twists": [["1.67.af", "1.4489.ef", 2], ["1.67.aq", "1.300763.abhw", 3], ["1.67.l", "1.300763.abhw", 3], ["1.67.al", "1.90458382169.ajvta", 6], ["1.67.q", "1.90458382169.ajvta", 6]], "weak_equivalence_count": 3, "zfv_index": 9, "zfv_index_factorization": [[3, 2]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_pic_size": 3, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 243, "zfv_singular_count": 2, "zfv_singular_primes": ["3,-F-1"]}