# Stored data for abelian variety isogeny class 2.19.a_u, downloaded from the LMFDB on 29 April 2026.
{"abvar_count": 382, "abvar_counts": [382, 145924, 47032222, 17067854736, 6131068049902, 2212029906257284, 799006686986012782, 288446745038400000000, 104127350297290285840222, 37589995432529113162209604], "abvar_counts_str": "382 145924 47032222 17067854736 6131068049902 2212029906257284 799006686986012782 288446745038400000000 104127350297290285840222 37589995432529113162209604 ", "angle_corank": 1, "angle_rank": 1, "angles": [0.33821351072027, 0.66178648927973], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 20, "curve_counts": [20, 402, 6860, 130966, 2476100, 47018562, 893871740, 16983876958, 322687697780, 6131069842002], "curve_counts_str": "20 402 6860 130966 2476100 47018562 893871740 16983876958 322687697780 6131069842002 ", "curves": ["y^2=8*x^6+5*x^5+5*x^4+2*x^3+4*x^2+18*x+12", "y^2=16*x^6+10*x^5+10*x^4+4*x^3+8*x^2+17*x+5", "y^2=13*x^6+15*x^5+16*x+9", "y^2=10*x^6+12*x^5+13*x^4+15*x^3+5*x^2+8*x+11", "y^2=x^6+5*x^5+7*x^4+11*x^3+10*x^2+16*x+3", "y^2=7*x^6+7*x^5+3*x^4+6*x^2+10*x+18", "y^2=5*x^6+11*x^5+4*x^4+8*x^2+13*x+2", "y^2=3*x^6+11*x^5+2*x^4+10*x^3+12*x^2+13*x+7", "y^2=6*x^6+3*x^5+4*x^4+x^3+5*x^2+7*x+14"], "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": ["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": ["2.0.116.1"], "geometric_splitting_field": "2.0.116.1", "geometric_splitting_polynomials": [[29, 0, 1]], "group_structure_count": 1, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 9, "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": 9, "label": "2.19.a_u", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 8, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [], "number_fields": ["4.0.215296.1"], "p": 19, "p_rank": 2, "p_rank_deficit": 0, "poly": [1, 0, 20, 0, 361], "poly_str": "1 0 20 0 361 ", "primitive_models": [], "q": 19, "real_poly": [1, 0, -18], "simple_distinct": ["2.19.a_u"], "simple_factors": ["2.19.a_uA"], "simple_multiplicities": [1], "singular_primes": ["3,-13*F^2-F-V+8"], "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.215296.1", "splitting_polynomials": [[225, 0, 28, 0, 1]], "twist_count": 4, "twists": [["2.19.a_au", "2.130321.yu_usyo", 4], ["2.19.ag_s", "2.16983563041.rwjs_hhsitfkw", 8], ["2.19.g_s", "2.16983563041.rwjs_hhsitfkw", 8]], "weak_equivalence_count": 2, "zfv_index": 9, "zfv_index_factorization": [[3, 2]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_plus_index": 3, "zfv_plus_index_factorization": [[3, 1]], "zfv_plus_norm": 3364, "zfv_singular_count": 2, "zfv_singular_primes": ["3,-13*F^2-F-V+8"]}