# Stored data for abelian variety isogeny class 2.32.an_dh, downloaded from the LMFDB on 01 May 2024.
{"label": "2.32.an_dh", "g": 2, "p": 2, "q": 32, "poly": [1, -13, 85, -416, 1024], "poly_str": "1 -13 85 -416 1024 ", "slopes": ["0A", "0B", "1A", "1B"], "p_rank": 2, "p_rank_deficit": 0, "angles": [0.0605291260617589, 0.446568083608104], "angle_rank": 2, "number_fields": ["4.0.4111025.1"], "galois_groups": ["4T3"], "center_dim": 4, "abvar_counts": [681, 1048059, 1069494156, 1096279146531, 1125384870777261, 1152929775757622976, 1180600350156794818281, 1208925184469691961987299, 1237939681139133492629980764, 1267650616637503188089791549299], "abvar_counts_str": "681 1048059 1069494156 1096279146531 1125384870777261 1152929775757622976 1180600350156794818281 1208925184469691961987299 1237939681139133492629980764 1267650616637503188089791549299 ", "abvar_count": 681, "curve_counts": [20, 1026, 32639, 1045490, 33539080, 1073749527, 34359992428, 1099511050114, 35184361909703, 1125899921416986], "curve_counts_str": "20 1026 32639 1045490 33539080 1073749527 34359992428 1099511050114 35184361909703 1125899921416986 ", "curve_count": 20, "has_jacobian": 1, "has_principal_polarization": 1, "geometric_extension_degree": 1, "geometric_center_dim": 4, "geometric_number_fields": ["4.0.4111025.1"], "geometric_galois_groups": ["4T3"], "primitive_models": [], "is_primitive": true, "twists": [["2.32.n_dh", "2.1024.b_achj", 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": ["2.32.an_dh"], "simple_multiplicities": [1], "simple_factors": ["2.32.an_dhA"], "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, -13, 21], "jacobian_count": 10, "curves": ["y^2+(x^3+(a^3+a)*x+a^3+a)*y=x^6+(a^4+a^2+a+1)*x^5+(a^4+a^2+a+1)*x^4+(a^4+a^3)*x^3+(a^3+a^2+a)*x^2+(a^4+a^3+a^2+1)*x+a^4+1", "y^2+(x^3+(a^3+a^2+a)*x+a^3+a^2+a)*y=x^6+(a^4+a^3)*x^5+(a^4+a^3)*x^4+(a^2+a+1)*x^3+(a^4+a^3+a^2+a)*x^2+(a^4+a^2+a)*x+a^3+a^2", "y^2+(x^3+(a+1)*x+a+1)*y=x^6+(a^3+a^2+1)*x^5+(a^3+a^2+1)*x^4+(a^2+a)*x^3+(a^2+1)*x^2+x+a^4+a+1", "y^2+(x^3+a^3*x+a^3)*y=x^6+(a^4+a^3+a^2)*x^5+(a^4+a^3+a^2)*x^4+(a^4+a^2+a+1)*x^3+(a^3+a)*x^2+(a^4+a^2)*x+a^2+1", "y^2+(x^3+(a^4+a^3+a)*x+a^4+a^3+a)*y=x^6+a^4*x^5+a^4*x^4+(a^4+a^3+1)*x^3+(a+1)*x^2+x+a^4+a^3+a^2+a", "y^2+(x^3+(a^4+a+1)*x+a^4+a+1)*y=x^6+(a^4+a^2+1)*x^5+(a^4+a^2+1)*x^4+(a^4+a^3+a^2)*x^3+a^3*x^2+(a^2+a)*x+a+1", "y^2+(x^3+(a^3+a^2)*x+a^3+a^2)*y=x^6+a^2*x^5+a^2*x^4+(a^4+a^2+a)*x^3+(a^4+a^3+a)*x^2+x+a^3+a^2+a", "y^2+(x^3+(a^4+a^3+a^2+a)*x+a^4+a^3+a^2+a)*y=x^6+(a^2+a+1)*x^5+(a^2+a+1)*x^4+(a^4+a^2+1)*x^3+(a^4+a+1)*x^2+(a^4+a^3+1)*x+a^4+a^3+a", "y^2+(x^3+(a^4+1)*x+a^4+1)*y=x^6+a*x^5+a*x^4+(a^4+a^3+a^2+1)*x^3+(a^3+a^2)*x^2+x+a^3+a", "y^2+(x^3+(a^2+1)*x+a^2+1)*y=x^6+(a^4+a^3+a+1)*x^5+(a^4+a^3+a+1)*x^4+(a^4+a^2)*x^3+(a^4+1)*x^2+x+a^3"], "hyp_count": 10, "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": 569, "geometric_splitting_field": "4.0.4111025.1", "splitting_field": "4.0.4111025.1", "geometric_splitting_polynomials": [[271, -149, 22, -1, 1]], "splitting_polynomials": [[271, -149, 22, -1, 1]], "is_squarefree": true, "is_geometrically_squarefree": true, "size": 20, "principal_polarization_count": 10, "pic_prime_gens": [[1, 3, 1, 10], [1, 3, 2, 10]]}