# Stored data for abelian variety isogeny class 2.19.a_bf, downloaded from the LMFDB on 06 October 2026.
{"abvar_count": 393, "abvar_counts": [393, 154449, 47042100, 16921586889, 6131061313953, 2212959172410000, 799006685094178233, 288448326666476832969, 104127350298390928170900, 37589912835451086832486209], "abvar_counts_str": "393 154449 47042100 16921586889 6131061313953 2212959172410000 799006685094178233 288448326666476832969 104127350298390928170900 37589912835451086832486209 ", "angle_corank": 1, "angle_rank": 1, "angles": [0.401848606133825, 0.598151393866175], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 20, "curve_counts": [20, 424, 6860, 129844, 2476100, 47038318, 893871740, 16983970084, 322687697780, 6131056370104], "curve_counts_str": "20 424 6860 129844 2476100 47038318 893871740 16983970084 322687697780 6131056370104 ", "curves": ["y^2=8*x^6+17*x^5+7*x^4+7*x^3+9*x^2+x+10", "y^2=16*x^6+15*x^5+14*x^4+14*x^3+18*x^2+2*x+1", "y^2=17*x^6+12*x^5+5*x^3+4*x^2+18*x+4", "y^2=15*x^6+5*x^5+10*x^3+8*x^2+17*x+8", "y^2=10*x^6+13*x^5+9*x^4+18*x^3+8*x^2+8*x+4", "y^2=x^6+7*x^5+18*x^4+17*x^3+16*x^2+16*x+8", "y^2=14*x^6+7*x^5+18*x^4+9*x^3+6*x^2+3*x+14", "y^2=9*x^6+14*x^5+17*x^4+18*x^3+12*x^2+6*x+9", "y^2=8*x^6+14*x^4+11*x^3+6*x^2+15*x+11", "y^2=16*x^6+9*x^4+3*x^3+12*x^2+11*x+3", "y^2=12*x^6+15*x^5+8*x^4+8*x^3+11*x^2+2*x+18", "y^2=10*x^6+7*x^5+11*x^4+17*x^3+9*x^2+13*x+14", "y^2=x^6+14*x^5+3*x^4+15*x^3+18*x^2+7*x+9", "y^2=12*x^6+16*x^5+10*x^4+4*x^3+11*x^2+11*x+8"], "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": ["4T2"], "geom_dim1_distinct": 1, "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": 2, "geometric_extension_degree": 2, "geometric_galois_groups": ["2T1"], "geometric_number_fields": ["2.0.483.1"], "geometric_splitting_field": "2.0.483.1", "geometric_splitting_polynomials": [[121, -1, 1]], "group_structure_count": 1, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 14, "is_cyclic": true, "is_geometrically_simple": false, "is_geometrically_squarefree": false, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 14, "label": "2.19.a_bf", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 4, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [], "number_fields": ["4.0.3732624.4"], "p": 19, "p_rank": 2, "p_rank_deficit": 0, "poly": [1, 0, 31, 0, 361], "poly_str": "1 0 31 0 361 ", "primitive_models": [], "q": 19, "real_poly": [1, 0, -7], "simple_distinct": ["2.19.a_bf"], "simple_factors": ["2.19.a_bfA"], "simple_multiplicities": [1], "singular_primes": [], "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.3732624.4", "splitting_polynomials": [[361, 0, 31, 0, 1]], "twist_count": 2, "twists": [["2.19.a_abf", "2.130321.ask_scbr", 4]], "weak_equivalence_count": 1, "zfv_index": 1, "zfv_index_factorization": [], "zfv_is_bass": true, "zfv_is_maximal": true, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 4761, "zfv_singular_count": 0, "zfv_singular_primes": []}