# Stored data for abelian variety isogeny class 2.19.ad_bk, downloaded from the LMFDB on 25 April 2026.
{"abvar_count": 338, "abvar_counts": [338, 154804, 47918936, 16903358368, 6126826949438, 2213386004330176, 798993769927044302, 288441877382070991488, 104127771969840898198712, 37589983068013507765862644], "abvar_counts_str": "338 154804 47918936 16903358368 6126826949438 2213386004330176 798993769927044302 288441877382070991488 104127771969840898198712 37589983068013507765862644 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 0, "angle_rank": 2, "angles": [0.366038693328952, 0.520517985919903], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 17, "curve_counts": [17, 425, 6986, 129705, 2474387, 47047394, 893857289, 16983590353, 322689004526, 6131067825305], "curve_counts_str": "17 425 6986 129705 2474387 47047394 893857289 16983590353 322689004526 6131067825305 ", "curves": ["y^2=11*x^6+12*x^5+8*x^4+18*x^3+x^2+16*x+4", "y^2=12*x^6+5*x^5+4*x^4+17*x^3+14*x^2+2*x+5", "y^2=4*x^6+16*x^5+3*x^4+13*x^3+4*x^2+2*x+18", "y^2=x^6+9*x^5+12*x^4+11*x^3+6*x^2+13*x+18", "y^2=8*x^6+10*x^5+11*x^4+14*x^3+11*x^2+6*x+4", "y^2=12*x^6+5*x^4+11*x^3+10*x^2+7*x+10", "y^2=12*x^6+9*x^5+15*x^4+7*x^3+15*x^2+2", "y^2=9*x^6+9*x^5+3*x^4+5*x^3+6*x^2+9*x+5", "y^2=9*x^6+11*x^5+x^4+10*x^3+14*x^2+15*x+7", "y^2=6*x^6+9*x^5+4*x^4+x^3+18*x^2+9*x+2", "y^2=x^6+7*x^5+17*x^4+18*x^3+12*x^2+x+14", "y^2=2*x^5+8*x^4+12*x^3+9*x^2+10*x+12"], "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": 1, "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": ["4.0.1384888.1"], "geometric_splitting_field": "4.0.1384888.1", "geometric_splitting_polynomials": [[338, -10, 33, -1, 1]], "group_structure_count": 1, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 12, "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": 12, "label": "2.19.ad_bk", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 2, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [], "number_fields": ["4.0.1384888.1"], "p": 19, "p_rank": 2, "p_rank_deficit": 0, "pic_prime_gens": [[1, 2, 1, 2], [1, 3, 1, 3], [1, 13, 1, 4]], "poly": [1, -3, 36, -57, 361], "poly_str": "1 -3 36 -57 361 ", "primitive_models": [], "principal_polarization_count": 12, "q": 19, "real_poly": [1, -3, -2], "simple_distinct": ["2.19.ad_bk"], "simple_factors": ["2.19.ad_bkA"], "simple_multiplicities": [1], "singular_primes": [], "size": 12, "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.1384888.1", "splitting_polynomials": [[338, -10, 33, -1, 1]], "twist_count": 2, "twists": [["2.19.d_bk", "2.361.cl_cmm", 2]], "weak_equivalence_count": 1, "zfv_index": 1, "zfv_index_factorization": [], "zfv_is_bass": true, "zfv_is_maximal": true, "zfv_pic_size": 12, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 4792, "zfv_singular_count": 0, "zfv_singular_primes": []}