# Stored data for abelian variety isogeny class 2.5.ab_ab, downloaded from the LMFDB on 21 June 2026.
{"abvar_count": 19, "abvar_counts": [19, 589, 13471, 438805, 9968464, 245966989, 6183697231, 152444806245, 3813996125059, 95381612955904], "abvar_counts_str": "19 589 13471 438805 9968464 245966989 6183697231 152444806245 3813996125059 95381612955904 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 0, "angle_rank": 2, "angles": [0.169335136474198, 0.720319309200702], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 5, "curve_counts": [5, 23, 107, 699, 3190, 15743, 79147, 390259, 1952765, 9767078], "curve_counts_str": "5 23 107 699 3190 15743 79147 390259 1952765 9767078 ", "curves": ["y^2=4*x^6+3*x^5+x^4+4*x^3+3*x^2+4*x+3", "y^2=4*x^6+4*x^4+4*x^3+3*x^2+2*x+2", "y^2=2*x^6+2*x^5+4*x^4+3*x^2+3"], "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": ["4T3"], "geom_dim1_distinct": 0, "geom_dim1_factors": 0, "geom_dim2_distinct": 1, "geom_dim2_factors": 1, "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": 4, "geometric_extension_degree": 1, "geometric_galois_groups": ["4T3"], "geometric_number_fields": ["4.0.1525.1"], "geometric_splitting_field": "4.0.1525.1", "geometric_splitting_polynomials": [[5, -5, 6, -2, 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": true, "is_geometrically_squarefree": true, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 3, "label": "2.5.ab_ab", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 2, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [], "number_fields": ["4.0.1525.1"], "p": 5, "p_rank": 2, "p_rank_deficit": 0, "pic_prime_gens": [[1, 5, 1, 2]], "poly": [1, -1, -1, -5, 25], "poly_str": "1 -1 -1 -5 25 ", "primitive_models": [], "principal_polarization_count": 3, "q": 5, "real_poly": [1, -1, -11], "simple_distinct": ["2.5.ab_ab"], "simple_factors": ["2.5.ab_abA"], "simple_multiplicities": [1], "singular_primes": ["3,-F-7*V+8"], "size": 3, "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.1525.1", "splitting_polynomials": [[5, -5, 6, -2, 1]], "twist_count": 2, "twists": [["2.5.b_ab", "2.25.ad_bp", 2]], "weak_equivalence_count": 2, "zfv_index": 9, "zfv_index_factorization": [[3, 2]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_pic_size": 2, "zfv_plus_index": 3, "zfv_plus_index_factorization": [[3, 1]], "zfv_plus_norm": 61, "zfv_singular_count": 2, "zfv_singular_primes": ["3,-F-7*V+8"]}