# Stored data for abelian variety isogeny class 2.19.d_bc, downloaded from the LMFDB on 30 January 2026.
{"abvar_count": 450, "abvar_counts": [450, 148500, 46672200, 16999092000, 6124615224750, 2212872752376000, 799108509054952350, 288441874175569488000, 104126771453770219559400, 37589982794217723131212500], "abvar_counts_str": "450 148500 46672200 16999092000 6124615224750 2212872752376000 799108509054952350 288441874175569488000 104126771453770219559400 37589982794217723131212500 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 0, "angle_rank": 2, "angles": [0.426318466620529, 0.69443002753289], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 23, "curve_counts": [23, 409, 6806, 130441, 2473493, 47036482, 893985647, 16983590161, 322685903954, 6131067780649], "curve_counts_str": "23 409 6806 130441 2473493 47036482 893985647 16983590161 322685903954 6131067780649 ", "curves": ["y^2=9*x^6+10*x^5+2*x^4+12*x^3+x^2+18*x+4", "y^2=15*x^6+11*x^5+x^4+12*x^3+11*x^2+3*x+8", "y^2=11*x^6+18*x^5+5*x^4+x^3+10*x^2+9*x+6", "y^2=11*x^6+17*x^5+7*x^4+4*x^3+9*x^2+18*x+10", "y^2=11*x^6+x^5+5*x^4+17*x^3+4*x^2+8*x+10", "y^2=14*x^6+16*x^5+11*x^4+6*x^3+2*x^2+9*x+16", "y^2=14*x^6+x^5+3*x^4+17*x^3+14*x^2+18*x+2", "y^2=8*x^6+17*x^3+7*x^2+15*x+3", "y^2=11*x^6+12*x^5+5*x^4+7*x^3+9*x^2+17*x", "y^2=12*x^6+10*x^5+7*x^4+8*x^3+17*x^2+11*x+15", "y^2=6*x^5+11*x^4+5*x^3+15*x^2+2*x+12", "y^2=17*x^6+11*x^5+5*x^4+15*x^3+14*x^2+12*x+9", "y^2=14*x^6+10*x^5+4*x^4+2*x^3+11*x^2+15*x+18", "y^2=11*x^6+4*x^5+7*x^4+11*x^3+10*x^2+2*x", "y^2=10*x^6+2*x^4+5*x^3+4*x+3", "y^2=11*x^6+11*x^5+x^4+10*x^3+10*x^2+16*x+1", "y^2=6*x^6+17*x^5+13*x^4+2*x^3+18*x^2+8*x+15", "y^2=7*x^6+11*x^5+x^4+6*x^3+8*x^2+15*x+14", "y^2=9*x^6+9*x^5+x^4+18*x^2+10*x+1", "y^2=4*x^6+17*x^5+7*x^4+15*x^3+6*x^2+5*x+17", "y^2=4*x^6+x^5+11*x^4+15*x^3+15*x^2+9*x+9", "y^2=13*x^6+17*x^5+14*x^4+11*x^3+14*x^2+16*x+12", "y^2=11*x^6+18*x^5+5*x^4+15*x^3+10*x^2+4*x+7", "y^2=7*x^6+14*x^5+10*x^4+14*x^3+6*x^2+12*x+7"], "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": 4, "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", "2.0.51.1"], "geometric_splitting_field": "4.0.166464.4", "geometric_splitting_polynomials": [[123, -30, 31, -2, 1]], "group_structure_count": 2, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 24, "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": 24, "label": "2.19.d_bc", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 2, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [3], "number_fields": ["2.0.8.1", "2.0.51.1"], "p": 19, "p_rank": 2, "p_rank_deficit": 0, "pic_prime_gens": [[1, 2, 1, 6], [2, 3, 1, 6], [2, 5, 1, 12], [2, 11, 1, 24]], "poly": [1, 3, 28, 57, 361], "poly_str": "1 3 28 57 361 ", "primitive_models": [], "principal_polarization_count": 30, "q": 19, "real_poly": [1, 3, -10], "simple_distinct": ["1.19.ac", "1.19.f"], "simple_factors": ["1.19.acA", "1.19.fA"], "simple_multiplicities": [1, 1], "singular_primes": ["3,-2*F-16", "7,-5*F^2-11*F-102"], "size": 150, "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.166464.4", "splitting_polynomials": [[123, -30, 31, -2, 1]], "twist_count": 4, "twists": [["2.19.ah_bw", "2.361.bv_bsu", 2], ["2.19.ad_bc", "2.361.bv_bsu", 2], ["2.19.h_bw", "2.361.bv_bsu", 2]], "weak_equivalence_count": 4, "zfv_index": 147, "zfv_index_factorization": [[3, 1], [7, 2]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_pic_size": 96, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 3672, "zfv_singular_count": 4, "zfv_singular_primes": ["3,-2*F-16", "7,-5*F^2-11*F-102"]}