# Stored data for abelian variety isogeny class 2.19.ak_bz, downloaded from the LMFDB on 29 July 2026.
{"abvar_count": 213, "abvar_counts": [213, 130569, 46774800, 16859199849, 6122283767853, 2213551925280000, 799063743815563173, 288442310363975783049, 104127192529352677789200, 37589990180663150170659609], "abvar_counts_str": "213 130569 46774800 16859199849 6122283767853 2213551925280000 799063743815563173 288442310363975783049 104127192529352677789200 37589990180663150170659609 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 0, "angle_rank": 2, "angles": [0.0769799514809562, 0.443626041963722], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 10, "curve_counts": [10, 364, 6820, 129364, 2472550, 47050918, 893935570, 16983615844, 322687208860, 6131068985404], "curve_counts_str": "10 364 6820 129364 2472550 47050918 893935570 16983615844 322687208860 6131068985404 ", "curves": ["y^2=16*x^6+7*x^4+12*x^3+x^2+8*x+4", "y^2=8*x^6+6*x^5+13*x^4+11*x^3+14*x^2+3*x+12", "y^2=6*x^6+8*x^5+13*x^4+4*x^3+6*x^2+14*x+16", "y^2=14*x^6+x^5+16*x^4+8*x^3+11*x^2+13*x+3", "y^2=13*x^6+3*x^5+15*x^4+18*x^3+11*x^2+16*x+13", "y^2=6*x^6+x^5+16*x^4+17*x^3+x^2+15*x+18"], "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": ["4.0.46224.1"], "geometric_splitting_field": "4.0.46224.1", "geometric_splitting_polynomials": [[33, -24, 15, 0, 1]], "group_structure_count": 1, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 6, "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": 6, "label": "2.19.ak_bz", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 2, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [], "number_fields": ["4.0.46224.1"], "p": 19, "p_rank": 2, "p_rank_deficit": 0, "pic_prime_gens": [[1, 3, 1, 2], [1, 23, 1, 2]], "poly": [1, -10, 51, -190, 361], "poly_str": "1 -10 51 -190 361 ", "primitive_models": [], "principal_polarization_count": 6, "q": 19, "real_poly": [1, -10, 13], "simple_distinct": ["2.19.ak_bz"], "simple_factors": ["2.19.ak_bzA"], "simple_multiplicities": [1], "singular_primes": ["2,-F^2-V+4"], "size": 6, "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.46224.1", "splitting_polynomials": [[33, -24, 15, 0, 1]], "twist_count": 2, "twists": [["2.19.k_bz", "2.361.c_asj", 2]], "weak_equivalence_count": 2, "zfv_index": 4, "zfv_index_factorization": [[2, 2]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_pic_size": 4, "zfv_plus_index": 2, "zfv_plus_index_factorization": [[2, 1]], "zfv_plus_norm": 321, "zfv_singular_count": 2, "zfv_singular_primes": ["2,-F^2-V+4"]}