# Stored data for abelian variety isogeny class 5.2.b_a_c_b_ad, downloaded from the LMFDB on 18 March 2026.
{"abvar_count": 60, "abvar_counts": [60, 720, 91260, 748800, 25491300, 1251722160, 48913421820, 1072353484800, 44005970532420, 1148255914395600], "abvar_counts_str": "60 720 91260 748800 25491300 1251722160 48913421820 1072353484800 44005970532420 1148255914395600 ", "angle_corank": 0, "angle_rank": 5, "angles": [0.12811090720544, 0.355275543655217, 0.48300065507736, 0.782684104099944, 0.955695839449801], "center_dim": 10, "cohen_macaulay_max": 1, "curve_count": 4, "curve_counts": [4, 4, 16, 12, 24, 76, 172, 252, 628, 1044], "curve_counts_str": "4 4 16 12 24 76 172 252 628 1044 ", "curves": ["y^2 + (x^4 + x^3 + x^2 + x + 1)*x*y = x^{12} + x", "x^4*y + x^3*y^2 + x^3*y*z + x^3*z^2 + x^2*y^3 + x^2*y*z^2 + x*y^2*z^2 + y^5 + y^4*z + y^3*z^2 + y^2*z^3", "x^4*y + x^4*z + x^3*y*z + x^2*y^3 + x^2*y*z^2 + x*y^4 + x*y^2*z^2 + x*y*z^3 + y^4*z", "x^4*z + x^3*y^2 + x^3*z^2 + x^2*y^3 + x^2*y^2*z + x^2*y*z^2 + x*y^3*z + y^5 + y^4*z + y^3*z^2 + y^2*z^3"], "dim1_distinct": 0, "dim1_factors": 0, "dim2_distinct": 0, "dim2_factors": 0, "dim3_distinct": 0, "dim3_factors": 0, "dim4_distinct": 0, "dim4_factors": 0, "dim5_distinct": 1, "dim5_factors": 1, "endomorphism_ring_count": 9, "g": 5, "galois_groups": ["10T39"], "geom_dim1_distinct": 0, "geom_dim1_factors": 0, "geom_dim2_distinct": 0, "geom_dim2_factors": 0, "geom_dim3_distinct": 0, "geom_dim3_factors": 0, "geom_dim4_distinct": 0, "geom_dim4_factors": 0, "geom_dim5_distinct": 1, "geom_dim5_factors": 1, "geometric_center_dim": 10, "geometric_extension_degree": 1, "geometric_galois_groups": ["10T39"], "geometric_number_fields": ["10.0.111140444342016.1"], "geometric_splitting_field": "10.0.111140444342016.1", "geometric_splitting_polynomials": [[32, -16, 0, -8, 2, 3, 1, -2, 0, -1, 1]], "group_structure_count": 2, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 1, "is_cyclic": false, "is_geometrically_simple": true, "is_geometrically_squarefree": true, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 4, "label": "5.2.b_a_c_b_ad", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 2, "newton_coelevation": 9, "newton_elevation": 0, "noncyclic_primes": [2], "number_fields": ["10.0.111140444342016.1"], "p": 2, "p_rank": 5, "p_rank_deficit": 0, "poly": [1, 1, 0, 2, 1, -3, 2, 8, 0, 16, 32], "poly_str": "1 1 0 2 1 -3 2 8 0 16 32 ", "primitive_models": [], "q": 2, "real_poly": [1, 1, -10, -6, 21, -3], "simple_distinct": ["5.2.b_a_c_b_ad"], "simple_factors": ["5.2.b_a_c_b_adA"], "simple_multiplicities": [1], "singular_primes": ["2,-F^4+6*F^2-3*V^4-5*V^3-4*V^2+6*V+6", "2,4*F^3-7*F^2-11*F+3*V^4+V^3-10*V^2-21*V-20"], "slopes": ["0A", "0B", "0C", "0D", "0E", "1A", "1B", "1C", "1D", "1E"], "splitting_field": "10.0.111140444342016.1", "splitting_polynomials": [[32, -16, 0, -8, 2, 3, 1, -2, 0, -1, 1]], "twist_count": 2, "twists": [["5.2.ab_a_ac_b_d", "5.4.ab_ac_g_ad_af", 2]], "weak_equivalence_count": 9, "zfv_index": 16, "zfv_index_factorization": [[2, 4]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_plus_index": 4, "zfv_plus_index_factorization": [[2, 2]], "zfv_plus_norm": 31, "zfv_singular_count": 4, "zfv_singular_primes": ["2,-F^4+6*F^2-3*V^4-5*V^3-4*V^2+6*V+6", "2,4*F^3-7*F^2-11*F+3*V^4+V^3-10*V^2-21*V-20"]}