# Stored data for abelian variety isogeny class 2.8.af_r, downloaded from the LMFDB on 01 May 2024.
{"label": "2.8.af_r", "g": 2, "p": 2, "q": 8, "poly": [1, -5, 17, -40, 64], "poly_str": "1 -5 17 -40 64 ", "slopes": ["0A", "0B", "1A", "1B"], "p_rank": 2, "p_rank_deficit": 0, "angles": [0.178413517577257, 0.48825314908941], "angle_rank": 1, "number_fields": ["4.0.441.1"], "galois_groups": ["4T2"], "center_dim": 4, "abvar_counts": [37, 4699, 268324, 16582771, 1082796157, 69244764736, 4403913768613, 281374617640419, 18012370805110276, 1152932336616165499], "abvar_counts_str": "37 4699 268324 16582771 1082796157 69244764736 4403913768613 281374617640419 18012370805110276 1152932336616165499 ", "abvar_count": 37, "curve_counts": [4, 74, 523, 4050, 33044, 264143, 2099948, 16771234, 134202619, 1073751914], "curve_counts_str": "4 74 523 4050 33044 264143 2099948 16771234 134202619 1073751914 ", "curve_count": 4, "has_jacobian": 1, "has_principal_polarization": 1, "geometric_extension_degree": 3, "geometric_center_dim": 2, "geometric_number_fields": ["2.0.7.1"], "geometric_galois_groups": ["2T1"], "primitive_models": [], "is_primitive": true, "twists": [["2.8.f_r", "2.64.j_r", 2], ["2.8.k_bp", "2.512.k_boj", 3], ["2.8.ak_bp", "2.262144.cyw_dipxp", 6], ["2.8.a_aj", "2.262144.cyw_dipxp", 6], ["2.8.f_r", "2.262144.cyw_dipxp", 6], ["2.8.a_j", "2.68719476736.acbxnm_btbiqmsqz", 12]], "twist_count": 6, "max_twist_degree": 12, "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "is_simple": true, "is_geometrically_simple": false, "simple_distinct": ["2.8.af_r"], "simple_multiplicities": [1], "simple_factors": ["2.8.af_rA"], "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": 2, "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": false, "real_poly": [1, -5, 1], "jacobian_count": 6, "curves": ["y^2+(x^3+(a+1)*x+a+1)*y=x^6+a^2*x^5+a^2*x^4+(a^2+1)*x^2+(a^2+1)*x+a^2+a+1", "y^2+(x^3+(a^2+1)*x+a^2+1)*y=x^6+(a^2+a)*x^5+(a^2+a)*x^4+(a^2+a+1)*x^2+(a^2+a+1)*x+a+1", "y^2+(x^3+(a^2+a+1)*x+a^2+a+1)*y=x^6+a*x^5+a*x^4+(a+1)*x^2+(a+1)*x+a^2+1", "y^2+(x^3+(a^2+1)*x+a^2+1)*y=(a^2+1)*x^5+(a^2+1)*x^4+a*x^3+a^2+a+1", "y^2+(x^3+(a+1)*x+a+1)*y=(a+1)*x^5+(a+1)*x^4+(a^2+a)*x^3+a^2+1", "y^2+(x^3+(a^2+a+1)*x+a^2+a+1)*y=(a^2+a+1)*x^5+(a^2+a+1)*x^4+a^2*x^3+a+1"], "hyp_count": 6, "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_index": 17, "zfv_index_factorization": [[17, 1]], "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 289, "geometric_splitting_field": "2.0.7.1", "splitting_field": "4.0.441.1", "geometric_splitting_polynomials": [[2, -1, 1]], "splitting_polynomials": [[4, -2, -1, -1, 1]], "is_squarefree": true, "is_geometrically_squarefree": false, "size": 4, "principal_polarization_count": 6, "pic_prime_gens": [[1, 2, 1, 3]]}