# Stored data for abelian variety isogeny class 1.491.az, downloaded from the LMFDB on 06 November 2025.
{"abvar_count": 467, "abvar_counts": [467, 241439, 118391972, 58120403275, 28536942302077, 14011639214435984, 6879714954162364207, 3377940044723416955475, 1658568561965901848788412, 814357163924330630046385679], "abvar_counts_str": "467 241439 118391972 58120403275 28536942302077 14011639214435984 6879714954162364207 3377940044723416955475 1658568561965901848788412 814357163924330630046385679 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 0, "angle_rank": 1, "angles": [0.30921664551838], "center_dim": 2, "curve_count": 467, "curve_counts": [467, 241439, 118391972, 58120403275, 28536942302077, 14011639214435984, 6879714954162364207, 3377940044723416955475, 1658568561965901848788412, 814357163924330630046385679], "curve_counts_str": "467 241439 118391972 58120403275 28536942302077 14011639214435984 6879714954162364207 3377940044723416955475 1658568561965901848788412 814357163924330630046385679 ", "curves": ["y^2=x^3+274*x+274", "y^2=x^3+223*x+446", "y^2=x^3+420*x+420", "y^2=x^3+279*x+67", "y^2=x^3+406*x+321", "y^2=x^3+366*x+366", "y^2=x^3+27*x+54", "y^2=x^3+474*x+474"], "dim1_distinct": 1, "dim1_factors": 1, "dim2_distinct": 0, "dim2_factors": 0, "dim3_distinct": 0, "dim3_factors": 0, "dim4_distinct": 0, "dim4_factors": 0, "dim5_distinct": 0, "dim5_factors": 0, "g": 1, "galois_groups": ["2T1"], "geom_dim1_distinct": 1, "geom_dim1_factors": 1, "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": 1, "geometric_galois_groups": ["2T1"], "geometric_number_fields": ["2.0.1339.1"], "geometric_splitting_field": "2.0.1339.1", "geometric_splitting_polynomials": [[335, -1, 1]], "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 0, "is_geometrically_simple": true, "is_geometrically_squarefree": true, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 8, "label": "1.491.az", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 2, "newton_coelevation": 1, "newton_elevation": 0, "number_fields": ["2.0.1339.1"], "p": 491, "p_rank": 1, "p_rank_deficit": 0, "poly": [1, -25, 491], "poly_str": "1 -25 491 ", "primitive_models": [], "principal_polarization_count": 8, "q": 491, "real_poly": [1, -25], "simple_distinct": ["1.491.az"], "simple_factors": ["1.491.azA"], "simple_multiplicities": [1], "size": 8, "slopes": ["0A", "1A"], "splitting_field": "2.0.1339.1", "splitting_polynomials": [[335, -1, 1]], "twist_count": 2, "twists": [["1.491.z", "1.241081.nt", 2]]}