# Stored data for abelian variety isogeny class 1.27.aj, downloaded from the LMFDB on 03 May 2024.
{"label": "1.27.aj", "g": 1, "p": 3, "q": 27, "poly": [1, -9, 27], "poly_str": "1 -9 27 ", "slopes": ["1/2A", "1/2B"], "p_rank": 0, "p_rank_deficit": 1, "angles": [0.166666666666667], "angle_rank": 0, "number_fields": ["2.0.3.1"], "galois_groups": ["2T1"], "center_dim": 2, "abvar_counts": [19, 703, 19684, 532171, 14355469, 387459856, 10460530351, 282430067923, 7625597484988, 205891117745743], "abvar_counts_str": "19 703 19684 532171 14355469 387459856 10460530351 282430067923 7625597484988 205891117745743 ", "abvar_count": 19, "curve_counts": [19, 703, 19684, 532171, 14355469, 387459856, 10460530351, 282430067923, 7625597484988, 205891117745743], "curve_counts_str": "19 703 19684 532171 14355469 387459856 10460530351 282430067923 7625597484988 205891117745743 ", "curve_count": 19, "has_jacobian": 1, "has_principal_polarization": 1, "geometric_extension_degree": 6, "geometric_center_dim": 1, "geometric_number_fields": ["1.1.1.1"], "geometric_galois_groups": ["1T1"], "primitive_models": [], "is_primitive": true, "twists": [["1.27.j", "1.729.abb", 2], ["1.27.a", "1.19683.a", 3], ["1.27.j", "1.19683.a", 3]], "twist_count": 3, "max_twist_degree": 3, "max_divalg_dim": 1, "max_geom_divalg_dim": 4, "is_simple": true, "is_geometrically_simple": true, "simple_distinct": ["1.27.aj"], "simple_multiplicities": [1], "simple_factors": ["1.27.ajA"], "dim1_factors": 1, "dim2_factors": 0, "dim3_factors": 0, "dim4_factors": 0, "dim5_factors": 0, "dim1_distinct": 1, "dim2_distinct": 0, "dim3_distinct": 0, "dim4_distinct": 0, "dim5_distinct": 0, "geom_dim1_factors": 1, "geom_dim2_factors": 0, "geom_dim3_factors": 0, "geom_dim4_factors": 0, "geom_dim5_factors": 0, "geom_dim1_distinct": 1, "geom_dim2_distinct": 0, "geom_dim3_distinct": 0, "geom_dim4_distinct": 0, "geom_dim5_distinct": 0, "has_geom_ss_factor": true, "real_poly": [1, -9], "jacobian_count": 1, "hyp_count": 1, "geometric_splitting_field": "1.1.1.1", "splitting_field": "2.0.3.1", "geometric_splitting_polynomials": [[0, 1]], "splitting_polynomials": [[1, -1, 1]], "is_squarefree": true, "is_geometrically_squarefree": true}