# Stored data for abelian variety isogeny class 2.32.aq_ep, downloaded from the LMFDB on 29 April 2024.
{"label": "2.32.aq_ep", "g": 2, "p": 2, "q": 32, "poly": [1, -16, 119, -512, 1024], "poly_str": "1 -16 119 -512 1024 ", "slopes": ["0A", "0B", "1A", "1B"], "p_rank": 2, "p_rank_deficit": 0, "angles": [0.0751336404065397, 0.354289791955075], "angle_rank": 2, "number_fields": ["2.0.7.1", "2.0.103.1"], "galois_groups": ["2T1", "2T1"], "center_dim": 4, "abvar_counts": [616, 1029952, 1076331256, 1098806351104, 1125459241405576, 1152845724814079296, 1180591858829696829208, 1208928540001101610521600, 1237940604968587464161921704, 1267650643727579038278197906752], "abvar_counts_str": "616 1029952 1076331256 1098806351104 1125459241405576 1152845724814079296 1180591858829696829208 1208928540001101610521600 1237940604968587464161921704 1267650643727579038278197906752 ", "abvar_count": 616, "curve_counts": [17, 1007, 32849, 1047903, 33541297, 1073671247, 34359745297, 1099514101951, 35184388166513, 1125899945477807], "curve_counts_str": "17 1007 32849 1047903 33541297 1073671247 34359745297 1099514101951 35184388166513 1125899945477807 ", "curve_count": 17, "has_jacobian": 1, "has_principal_polarization": 1, "geometric_extension_degree": 1, "geometric_center_dim": 4, "geometric_number_fields": ["2.0.7.1", "2.0.103.1"], "geometric_galois_groups": ["2T1", "2T1"], "primitive_models": [], "is_primitive": true, "twists": [["2.32.ag_j", "2.1024.as_agt", 2], ["2.32.g_j", "2.1024.as_agt", 2], ["2.32.q_ep", "2.1024.as_agt", 2]], "twist_count": 4, "max_twist_degree": 2, "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "is_simple": false, "is_geometrically_simple": false, "simple_distinct": ["1.32.al", "1.32.af"], "simple_multiplicities": [1, 1], "simple_factors": ["1.32.alA", "1.32.afA"], "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": 2, "geom_dim2_distinct": 0, "geom_dim3_distinct": 0, "geom_dim4_distinct": 0, "geom_dim5_distinct": 0, "has_geom_ss_factor": false, "real_poly": [1, -16, 55], "jacobian_count": 25, "curves": ["y^2+(x^2+x+1)*y=a^4*x^5+x^4+a^4*x^3+(a^4+a^3+a)*x^2+(a^3+a+1)*x+a^4+a^3+a", "y^2+(x^2+x+a+1)*y=(a^4+a)*x^5+x^4+(a^3+a+1)*x^3+x^2+(a^2+a+1)*x+a^3+a+1", "y^2+(x^2+x+a^3+a^2+a)*y=(a^3+1)*x^5+x^4+(a^4+a^2)*x^3+x^2+(a^4+a^3+a^2+a+1)*x+a^3+1", "y^2+(x^2+x+1)*y=a*x^5+x^4+a*x^3+(a^4+1)*x^2+(a^4+a)*x+a^4+1", "y^2+(x^2+x+a^3+a^2)*y=(a^3+a^2+a+1)*x^5+x^4+(a^4+a)*x^3+x^2+(a^4+a^2+a+1)*x+a^4+a", "y^2+(x^2+x+1)*y=(a^3+a^2+1)*x^5+x^4+(a^3+a^2+1)*x^3+(a+1)*x^2+(a^3+a^2+a+1)*x+a+1", "y^2+(x^2+x+a^2+1)*y=(a^3+1)*x^5+x^4+(a^3+a^2+a+1)*x^3+x^2+(a^4+a^2+1)*x+a^3+a^2+a+1", "y^2+(x^2+x)*y=a^2*x^5+(a^4+1)*x^3+(a^2+1)*x^2+a^4*x", "y^2+(x^2+x)*y=(a^3+a^2+1)*x^5+(a^4+a^3+a)*x^3+(a^3+a^2)*x^2+(a^4+a^3+a+1)*x", "y^2+(x^2+x+a^4+a^3+a^2+a)*y=(a^3+a+1)*x^5+x^4+(a^4+a^3+a^2+1)*x^3+x^2+(a^4+a)*x+a^3+a+1", "y^2+(x^2+x)*y=a^3*x^5+(a^4+a^3+a^2)*x^3+(a^3+1)*x^2+(a^4+a^3+a^2+1)*x", "y^2+(x^2+x+1)*y=a^2*x^5+x^4+a^2*x^3+(a^3+a^2)*x^2+(a^3+1)*x+a^3+a^2", "y^2+(x^2+x+a^4+a^3+a)*y=(a^4+a^3+a^2+a+1)*x^5+x^4+(a^3+1)*x^3+x^2+(a^4+a^3)*x+a^3+1", "y^2+(x^2+x+a^3+a)*y=(a^4+a)*x^5+x^4+(a^2+a)*x^3+x^2+(a^3+a^2+a+1)*x+a^4+a", "y^2+(x^2+x+1)*y=(a^4+a^3+a+1)*x^5+x^4+(a^4+a^3+a+1)*x^3+(a^2+1)*x^2+(a^4+a^3+a^2+a+1)*x+a^2+1", "y^2+(x^2+x+a^4+1)*y=(a^3+a+1)*x^5+x^4+(a^4+a^3+a^2+a+1)*x^3+x^2+(a^4+a^3+a^2)*x+a^4+a^3+a^2+a+1", "y^2+(x^2+x)*y=a*x^5+(a^2+1)*x^3+(a+1)*x^2+a^2*x", "y^2+(x^2+x)*y=a^4*x^5+(a^3+a^2)*x^3+(a^4+1)*x^2+(a^3+a^2+1)*x", "y^2+(x^2+x)*y=(a^4+a^2)*x^5+(a^4+a^2+1)*x^3+(a^4+a)*x^2+(a^4+a+1)*x", "y^2+(x^2+x+a^3)*y=(a^4+a^3+a^2+a+1)*x^5+x^4+(a^4+a^3+1)*x^3+x^2+(a^3+a+1)*x+a^4+a^3+a^2+a+1", "y^2+(x^2+x)*y=a*x^5+x^4+(a+1)*x^3+(a^4+a^3+a)*x^2+(a^4+a^3+a)*x", "y^2+(x^2+x)*y=(a^4+a^3+a^2+a+1)*x^5+x^4+(a^2+a+1)*x^3+(a^4+a^3+a^2+a+1)*x^2+(a^2+a)*x", "y^2+(x^2+x+a^4+a+1)*y=(a^3+a^2+a+1)*x^5+x^4+(a^4+a^2+a)*x^3+x^2+(a^3+1)*x+a^3+a^2+a+1", "y^2+(x^2+x)*y=(a^3+a^2+a)*x^5+x^4+(a^4+a^3)*x^3+(a^4+a^3)*x^2+(a^3+a^2+a+1)*x", "y^2+(x^2+x)*y=(a^3+a)*x^5+x^4+(a^4+a^2+a+1)*x^3+(a^4+a^2+a+1)*x^2+(a^3+a+1)*x"], "hyp_count": 25, "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_index": 36, "zfv_index_factorization": [[2, 2], [3, 2]], "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 721, "geometric_splitting_field": "4.0.519841.1", "splitting_field": "4.0.519841.1", "geometric_splitting_polynomials": [[576, 0, 55, 0, 1]], "splitting_polynomials": [[576, 0, 55, 0, 1]], "is_squarefree": true, "is_geometrically_squarefree": true, "size": 100, "principal_polarization_count": 30, "pic_prime_gens": [[1, 7, 1, 2], [2, 7, 1, 5], [1, 11, 1, 4]]}