# Stored data for abelian variety isogeny class 2.32.a_a, downloaded from the LMFDB on 17 May 2024.
{"label": "2.32.a_a", "g": 2, "p": 2, "q": 32, "poly": [1, 0, 0, 0, 1024], "poly_str": "1 0 0 0 1024 ", "slopes": ["1/2A", "1/2B", "1/2C", "1/2D"], "p_rank": 0, "p_rank_deficit": 2, "angles": [0.25, 0.75], "angle_rank": 0, "number_fields": ["2.0.4.1", "2.0.4.1"], "galois_groups": ["2T1", "2T1"], "center_dim": 4, "abvar_counts": [1025, 1050625, 1073741825, 1103812890625, 1125899906842625, 1152921506754330625, 1180591620717411303425, 1208921207935207812890625, 1237940039285380274899124225, 1267650600228231653296516890625], "abvar_counts_str": "1025 1050625 1073741825 1103812890625 1125899906842625 1152921506754330625 1180591620717411303425 1208921207935207812890625 1237940039285380274899124225 1267650600228231653296516890625 ", "abvar_count": 1025, "curve_counts": [33, 1025, 32769, 1052673, 33554433, 1073741825, 34359738369, 1099507433473, 35184372088833, 1125899906842625], "curve_counts_str": "33 1025 32769 1052673 33554433 1073741825 34359738369 1099507433473 35184372088833 1125899906842625 ", "curve_count": 33, "has_jacobian": 1, "has_principal_polarization": 1, "geometric_extension_degree": 4, "geometric_center_dim": 1, "geometric_number_fields": ["1.1.1.1"], "geometric_galois_groups": ["1T1"], "primitive_models": ["2.2.a_a"], "is_primitive": false, "twists": [["2.32.aq_ey", "2.1024.a_dau", 2], ["2.32.q_ey", "2.1024.a_dau", 2], ["2.32.ai_bg", "2.1073741824.a_gytisyy", 6], ["2.32.i_bg", "2.1073741824.a_gytisyy", 6], ["2.32.ai_cm", "2.1099511627776.ajeqpk_bfpjopkats", 8], ["2.32.a_acm", "2.1099511627776.ajeqpk_bfpjopkats", 8], ["2.32.a_cm", "2.1099511627776.ajeqpk_bfpjopkats", 8], ["2.32.i_cm", "2.1099511627776.ajeqpk_bfpjopkats", 8], ["2.32.a_abg", "2.1329227995784915872903807060280344576.abwimhgjsygfdee_bhruayrmkznstexrbbtujvliizg", 24], ["2.32.a_bg", "2.1329227995784915872903807060280344576.abwimhgjsygfdee_bhruayrmkznstexrbbtujvliizg", 24]], "twist_count": 11, "max_twist_degree": 24, "max_divalg_dim": 1, "max_geom_divalg_dim": 4, "is_simple": false, "is_geometrically_simple": false, "simple_distinct": ["1.32.ai", "1.32.i"], "simple_multiplicities": [1, 1], "simple_factors": ["1.32.aiA", "1.32.iA"], "dim1_factors": 2, "dim2_factors": 0, "dim3_factors": 0, "dim4_factors": 0, "dim5_factors": 0, "dim1_distinct": 2, "dim2_distinct": 0, "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": true, "real_poly": [1, 0, -64], "jacobian_count": 31, "curves": ["y^2+y=x^5", "y^2+y=(a^4+a+1)*x^5+x^4+(a^4+a+1)*x^3", "y^2+y=(a+1)*x^5+(a+1)*x^3", "y^2+y=(a+1)*x^5+a^2*x^4+(a+1)*x^3", "y^2+y=(a+1)*x^5+(a^2+1)*x^4+(a+1)*x^3", "y^2+y=a^3*x^5+x^4+a^3*x^3", "y^2+y=(a^3+a^2)*x^5+(a^3+a^2)*x^3", "y^2+y=(a^3+a^2)*x^5+(a^3+a+1)*x^4+(a^3+a^2)*x^3", "y^2+y=(a^3+a^2)*x^5+(a^3+a)*x^4+(a^3+a^2)*x^3", "y^2+y=(a^2+1)*x^5+(a^2+1)*x^3", "y^2+y=(a^2+1)*x^5+a^2*x^4+(a^2+1)*x^3", "y^2+y=(a^2+1)*x^5+(a^2+1)*x^4+(a^2+1)*x^3", "y^2+y=(a^4+a^3)*x^5+(a^4+a^3)*x^3", "y^2+y=(a^3+a)*x^5+x^4+(a^3+a)*x^3", "y^2+y=(a^4+a^2+1)*x^5+(a^4+a^2+1)*x^3", "y^2+y=(a^3+a^2+a+1)*x^5+a^3*x^4+(a^3+a^2+a+1)*x^3", "y^2+y=(a^4+a^3+a^2+a)*x^5+x^4+(a^4+a^3+a^2+a)*x^3", "y^2+y=(a^4+a^3+a)*x^5+(a^4+a^3+a)*x^3", "y^2+y=(a^4+a^3+a)*x^5+a*x^4+(a^4+a^3+a)*x^3", "y^2+y=(a^4+a^3+a)*x^5+(a+1)*x^4+(a^4+a^3+a)*x^3", "y^2+y=(a^4+1)*x^5+(a^4+1)*x^3", "y^2+y=(a^4+1)*x^5+a^4*x^4+(a^4+1)*x^3", "y^2+y=(a^4+1)*x^5+(a^4+1)*x^4+(a^4+1)*x^3", "y^2+y=(a^4+a^2+a+1)*x^5+(a^4+a^2+a+1)*x^3", "y^2+y=(a^2+a+1)*x^5+(a^2+a+1)*x^3", "y^2+y=(a^3+a+1)*x^5+a*x^4+(a^3+a+1)*x^3", "y^2+y=(a^3+a^2+a)*x^5+x^4+(a^3+a^2+a)*x^3", "y^2+y=(a^4+a^3+a^2)*x^5+(a^4+a^3+a^2)*x^3", "y^2+y=(a^3+1)*x^5+a^3*x^4+(a^3+1)*x^3", "y^2+y=(a^4+a)*x^5+a^4*x^4+(a^4+a)*x^3", "y^2+y=(a^4+a^3+a^2+a+1)*x^5+a^4*x^4+(a^4+a^3+a^2+a+1)*x^3"], "hyp_count": 31, "geometric_splitting_field": "1.1.1.1", "splitting_field": "2.0.4.1", "geometric_splitting_polynomials": [[0, 1]], "splitting_polynomials": [[1, 0, 1]], "is_squarefree": true, "is_geometrically_squarefree": false}