# Stored data for abelian variety isogeny class 2.19.ab_bk, downloaded from the LMFDB on 07 October 2026.
{"abvar_count": 378, "abvar_counts": [378, 158004, 47396664, 16843226400, 6128166765798, 2213929646824896, 799021550978054838, 288439958421504489600, 104127345957440010149784, 37589965309063951248484404], "abvar_counts_str": "378 158004 47396664 16843226400 6128166765798 2213929646824896 799021550978054838 288439958421504489600 104127345957440010149784 37589965309063951248484404 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 0, "angle_rank": 2, "angles": [0.426318466620529, 0.536593197520164], "center_dim": 4, "cohen_macaulay_max": 2, "curve_count": 19, "curve_counts": [19, 433, 6910, 129241, 2474929, 47058946, 893888371, 16983477361, 322687684330, 6131064928753], "curve_counts_str": "19 433 6910 129241 2474929 47058946 893888371 16983477361 322687684330 6131064928753 ", "curves": ["y^2=12*x^6+2*x^5+4*x^4+9*x^3+17*x^2+4*x+2", "y^2=5*x^6+12*x^5+17*x^4+16*x^3+4*x^2+12*x+17", "y^2=3*x^6+17*x^5+6*x^4+17*x^3+7*x^2+18*x+3", "y^2=4*x^6+2*x^5+9*x^4+10*x^3+14*x^2+17*x+5", "y^2=12*x^6+2*x^5+x^4+15*x^3+14*x^2+13*x+6", "y^2=9*x^6+5*x^5+6*x^4+14*x^3+16*x+9", "y^2=17*x^6+16*x^5+5*x^4+3*x^3+16*x^2+18*x+9"], "dim1_distinct": 2, "dim1_factors": 2, "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": 12, "g": 2, "galois_groups": ["2T1", "2T1"], "geom_dim1_distinct": 2, "geom_dim1_factors": 2, "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": 4, "geometric_extension_degree": 1, "geometric_galois_groups": ["2T1", "2T1"], "geometric_number_fields": ["2.0.8.1", "2.0.3.1"], "geometric_splitting_field": "4.0.576.1", "geometric_splitting_polynomials": [[4, 0, -2, 0, 1]], "group_structure_count": 3, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 7, "is_cyclic": false, "is_geometrically_simple": false, "is_geometrically_squarefree": true, "is_primitive": true, "is_simple": false, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 7, "label": "2.19.ab_bk", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 6, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [3], "number_fields": ["2.0.8.1", "2.0.3.1"], "p": 19, "p_rank": 2, "p_rank_deficit": 0, "pic_prime_gens": [[1, 2, 1, 2], [2, 7, 1, 6]], "poly": [1, -1, 36, -19, 361], "poly_str": "1 -1 36 -19 361 ", "primitive_models": [], "principal_polarization_count": 16, "q": 19, "real_poly": [1, -1, -2], "simple_distinct": ["1.19.ac", "1.19.b"], "simple_factors": ["1.19.acA", "1.19.bA"], "simple_multiplicities": [1, 1], "singular_primes": ["3,F+11", "5,7*V-9"], "size": 41, "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.576.1", "splitting_polynomials": [[4, 0, -2, 0, 1]], "twist_count": 12, "twists": [["2.19.ad_bo", "2.361.ct_cye", 2], ["2.19.b_bk", "2.361.ct_cye", 2], ["2.19.d_bo", "2.361.ct_cye", 2], ["2.19.ak_cc", "2.6859.by_lni", 3], ["2.19.f_y", "2.6859.by_lni", 3], ["2.19.aj_ca", "2.47045881.tim_kdjtvy", 6], ["2.19.ag_w", "2.47045881.tim_kdjtvy", 6], ["2.19.af_y", "2.47045881.tim_kdjtvy", 6], ["2.19.g_w", "2.47045881.tim_kdjtvy", 6], ["2.19.j_ca", "2.47045881.tim_kdjtvy", 6], ["2.19.k_cc", "2.47045881.tim_kdjtvy", 6]], "weak_equivalence_count": 14, "zfv_index": 135, "zfv_index_factorization": [[3, 3], [5, 1]], "zfv_is_bass": false, "zfv_is_maximal": false, "zfv_pic_size": 12, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 5400, "zfv_singular_count": 4, "zfv_singular_primes": ["3,F+11", "5,7*V-9"]}