# Stored data for abelian variety isogeny class 1.41.ak, downloaded from the LMFDB on 16 December 2025.
{"abvar_count": 32, "abvar_counts": [32, 1664, 69152, 2828800, 115877152, 4750189184, 194754264352, 7984921651200, 327381899005472, 13422659102962304], "abvar_counts_str": "32 1664 69152 2828800 115877152 4750189184 194754264352 7984921651200 327381899005472 13422659102962304 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 0, "angle_rank": 1, "angles": [0.214776712522723], "center_dim": 2, "cohen_macaulay_max": 1, "curve_count": 32, "curve_counts": [32, 1664, 69152, 2828800, 115877152, 4750189184, 194754264352, 7984921651200, 327381899005472, 13422659102962304], "curve_counts_str": "32 1664 69152 2828800 115877152 4750189184 194754264352 7984921651200 327381899005472 13422659102962304 ", "curves": ["y^2=x^3+34*x+34", "y^2=x^3+18*x+18", "y^2=x^3+24*x+31", "y^2=x^3+x"], "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": ["2.0.4.1"], "geometric_splitting_field": "2.0.4.1", "geometric_splitting_polynomials": [[1, 0, 1]], "group_structure_count": 3, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 0, "is_cyclic": false, "is_geometrically_simple": true, "is_geometrically_squarefree": true, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 4, "label": "1.41.ak", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 4, "newton_coelevation": 1, "newton_elevation": 0, "noncyclic_primes": [2], "number_fields": ["2.0.4.1"], "p": 41, "p_rank": 1, "p_rank_deficit": 0, "poly": [1, -10, 41], "poly_str": "1 -10 41 ", "primitive_models": [], "principal_polarization_count": 4, "q": 41, "real_poly": [1, -10], "simple_distinct": ["1.41.ak"], "simple_factors": ["1.41.akA"], "simple_multiplicities": [1], "singular_primes": ["2,F-1"], "size": 4, "slopes": ["0A", "1A"], "splitting_field": "2.0.4.1", "splitting_polynomials": [[1, 0, 1]], "twist_count": 4, "twists": [["1.41.k", "1.1681.as", 2], ["1.41.ai", "1.2825761.emw", 4], ["1.41.i", "1.2825761.emw", 4]], "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": 64, "zfv_singular_count": 2, "zfv_singular_primes": ["2,F-1"]}