# Stored data for abelian variety isogeny class 2.25.ao_ds, downloaded from the LMFDB on 07 May 2024.
{"label": "2.25.ao_ds", "g": 2, "p": 5, "q": 25, "poly": [1, -14, 96, -350, 625], "poly_str": "1 -14 96 -350 625 ", "slopes": ["0A", "0B", "1A", "1B"], "p_rank": 2, "p_rank_deficit": 0, "angles": [0.1620374772642, 0.323393582701288], "angle_rank": 2, "number_fields": ["4.0.247104.1"], "galois_groups": ["4T3"], "center_dim": 4, "abvar_counts": [358, 388788, 247888150, 153103159248, 95396013782278, 59604748800038100, 37253128482259302838, 23283167783149082784768, 14551931489736563015039350, 9094947711858931001642353428], "abvar_counts_str": "358 388788 247888150 153103159248 95396013782278 59604748800038100 37253128482259302838 23283167783149082784768 14551931489736563015039350 9094947711858931001642353428 ", "abvar_count": 358, "curve_counts": [12, 622, 15864, 391942, 9768552, 244141054, 6103552572, 152588568382, 3814701528444, 95367438919102], "curve_counts_str": "12 622 15864 391942 9768552 244141054 6103552572 152588568382 3814701528444 95367438919102 ", "curve_count": 12, "has_jacobian": 1, "has_principal_polarization": 1, "geometric_extension_degree": 1, "geometric_center_dim": 4, "geometric_number_fields": ["4.0.247104.1"], "geometric_galois_groups": ["4T3"], "primitive_models": [], "is_primitive": true, "twists": [["2.25.o_ds", "2.625.ae_zq", 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": ["2.25.ao_ds"], "simple_multiplicities": [1], "simple_factors": ["2.25.ao_dsA"], "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, 46], "jacobian_count": 8, "curves": ["y^2=(2*a+4)*x^6+(3*a+3)*x^5+(2*a+1)*x^4+(a+4)*x^3+a*x^2+(3*a+3)*x+4*a+4", "y^2=(a+4)*x^6+(4*a+2)*x^5+a*x^4+(a+1)*x^3+(2*a+4)*x^2+4*a*x+2*a+4", "y^2=(a+2)*x^6+(4*a+1)*x^4+(2*a+4)*x^3+(3*a+3)*x^2+(a+1)*x+3*a", "y^2=(4*a+1)*x^6+3*x^5+(4*a+4)*x^4+a*x^2+4*x+3*a+1", "y^2=(4*a+1)*x^6+(3*a+3)*x^5+x^4+(2*a+4)*x^3+4*a*x^2+3*x+a+4", "y^2=(3*a+2)*x^5+(2*a+1)*x^4+(3*a+2)*x^3+(3*a+2)*x^2+(a+3)*x", "y^2=(3*a+1)*x^6+(4*a+2)*x^5+3*x^4+(a+3)*x^3+3*a*x^2+(4*a+3)*x+a+1", "y^2=(2*a+1)*x^6+x^5+(3*a+1)*x^4+(a+4)*x^3+(3*a+3)*x^2+(a+2)*x+3*a"], "hyp_count": 8, "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": 1716, "geometric_splitting_field": "4.0.247104.1", "splitting_field": "4.0.247104.1", "geometric_splitting_polynomials": [[121, -2, 24, -2, 1]], "splitting_polynomials": [[121, -2, 24, -2, 1]], "is_squarefree": true, "is_geometrically_squarefree": true, "size": 8, "principal_polarization_count": 8, "pic_prime_gens": [[1, 2, 1, 2], [1, 3, 1, 2], [1, 11, 1, 2]]}