# Stored data for abelian variety isogeny class 2.27.ao_dx, downloaded from the LMFDB on 03 May 2024.
{"label": "2.27.ao_dx", "g": 2, "p": 3, "q": 27, "poly": [1, -14, 101, -378, 729], "poly_str": "1 -14 101 -378 729 ", "slopes": ["0A", "0B", "1A", "1B"], "p_rank": 2, "p_rank_deficit": 0, "angles": [0.19965256605425, 0.319371619550473], "angle_rank": 2, "number_fields": ["4.0.182848.5"], "galois_groups": ["4T3"], "center_dim": 4, "abvar_counts": [439, 536897, 394648708, 283555170889, 205967278901999, 150092305683567248, 109418086016687170343, 79766404396394534336457, 58149742052062799892262948, 42391157214746074368079015697], "abvar_counts_str": "439 536897 394648708 283555170889 205967278901999 150092305683567248 109418086016687170343 79766404396394534336457 58149742052062799892262948 42391157214746074368079015697 ", "abvar_count": 439, "curve_counts": [14, 736, 20048, 533556, 14354214, 387414478, 10460266866, 282429399524, 7625598147104, 205891126944016], "curve_counts_str": "14 736 20048 533556 14354214 387414478 10460266866 282429399524 7625598147104 205891126944016 ", "curve_count": 14, "has_jacobian": 1, "has_principal_polarization": 1, "geometric_extension_degree": 1, "geometric_center_dim": 4, "geometric_number_fields": ["4.0.182848.5"], "geometric_galois_groups": ["4T3"], "primitive_models": [], "is_primitive": true, "twists": [["2.27.o_dx", "2.729.g_bpj", 2]], "twist_count": 2, "max_twist_degree": 2, "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "is_simple": true, "is_geometrically_simple": true, "simple_distinct": ["2.27.ao_dx"], "simple_multiplicities": [1], "simple_factors": ["2.27.ao_dxA"], "dim1_factors": 0, "dim2_factors": 1, "dim3_factors": 0, "dim4_factors": 0, "dim5_factors": 0, "dim1_distinct": 0, "dim2_distinct": 1, "dim3_distinct": 0, "dim4_distinct": 0, "dim5_distinct": 0, "geom_dim1_factors": 0, "geom_dim2_factors": 1, "geom_dim3_factors": 0, "geom_dim4_factors": 0, "geom_dim5_factors": 0, "geom_dim1_distinct": 0, "geom_dim2_distinct": 1, "geom_dim3_distinct": 0, "geom_dim4_distinct": 0, "geom_dim5_distinct": 0, "has_geom_ss_factor": false, "real_poly": [1, -14, 47], "jacobian_count": 3, "curves": ["y^2=a*x^6+(2*a^2+a+1)*x^5+(2*a+2)*x^3+(2*a+1)*x^2+x+a^2+a+2", "y^2=(a^2+2*a+2)*x^6+(2*a^2+a+2)*x^5+(2*a^2+1)*x^4+(a+1)*x^3+(2*a^2+2*a+1)*x^2+a^2*x+a+2", "y^2=(2*a^2+2*a)*x^6+a*x^5+(a^2+2*a+1)*x^4+2*a^2*x^3+(2*a+1)*x^2+(a^2+2)*x+a^2+a+1"], "hyp_count": 3, "zfv_is_bass": true, "zfv_is_maximal": true, "zfv_index": 1, "zfv_index_factorization": [], "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 2857, "geometric_splitting_field": "4.0.182848.5", "splitting_field": "4.0.182848.5", "geometric_splitting_polynomials": [[193, -14, 29, -2, 1]], "splitting_polynomials": [[193, -14, 29, -2, 1]], "is_squarefree": true, "is_geometrically_squarefree": true, "size": 3, "principal_polarization_count": 3, "pic_prime_gens": [[1, 3, 1, 3]]}