# Stored data for abelian variety isogeny class 2.31.f_co, downloaded from the LMFDB on 14 September 2026.
{"abvar_count": 1188, "abvar_counts": [1188, 1031184, 875674800, 851052654144, 820057113807228, 787676838268320000, 756933639677873742348, 727423480000698735792384, 699053772090367845961009200, 671790517590032836625280896784], "abvar_counts_str": "1188 1031184 875674800 851052654144 820057113807228 787676838268320000 756933639677873742348 727423480000698735792384 699053772090367845961009200 671790517590032836625280896784 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 0, "angle_rank": 2, "angles": [0.528623632521575, 0.616954024640961], "center_dim": 4, "cohen_macaulay_max": 2, "curve_count": 37, "curve_counts": [37, 1069, 29392, 921529, 28644127, 887519518, 27512239897, 852891457489, 26439627913072, 819628273280629], "curve_counts_str": "37 1069 29392 921529 28644127 887519518 27512239897 852891457489 26439627913072 819628273280629 ", "curves": ["y^2=28*x^6+4*x^5+24*x^4+21*x^3+19*x^2+8*x+7", "y^2=22*x^6+11*x^5+23*x^4+8*x^3+25*x^2+2*x+28", "y^2=5*x^6+29*x^5+17*x^4+26*x^3+9*x^2+19*x+19", "y^2=15*x^6+26*x^5+30*x^4+26*x^3+30*x^2+19*x+12", "y^2=12*x^6+10*x^5+7*x^4+14*x^3+27*x^2+6*x+23", "y^2=22*x^5+15*x^4+27*x^3+30*x^2+4*x+20", "y^2=18*x^6+5*x^5+30*x^4+23*x^3+2*x^2+9*x+28", "y^2=28*x^6+21*x^5+22*x^4+19*x^3+6*x^2+16", "y^2=18*x^6+20*x^5+2*x^4+22*x^3+28*x^2+9*x+2", "y^2=18*x^6+16*x^5+28*x^4+21*x^3+24*x^2+14*x+5", "y^2=9*x^6+9*x^5+17*x^4+20*x^3+19*x^2+5*x+15", "y^2=9*x^6+12*x^5+28*x^4+14*x^3+30*x^2+20*x+28"], "dim1_distinct": 2, "dim1_factors": 2, "dim2_distinct": 0, "dim2_factors": 0, "dim3_distinct": 0, "dim3_factors": 0, "dim4_distinct": 0, "dim4_factors": 0, "dim5_distinct": 0, "dim5_factors": 0, "endomorphism_ring_count": 10, "g": 2, "galois_groups": ["2T1", "2T1"], "geom_dim1_distinct": 2, "geom_dim1_factors": 2, "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": 0, "geom_dim5_factors": 0, "geometric_center_dim": 4, "geometric_extension_degree": 1, "geometric_galois_groups": ["2T1", "2T1"], "geometric_number_fields": ["2.0.123.1", "2.0.3.1"], "geometric_splitting_field": "4.0.15129.1", "geometric_splitting_polynomials": [[100, 10, 11, -1, 1]], "group_structure_count": 6, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 12, "is_cyclic": false, "is_geometrically_simple": false, "is_geometrically_squarefree": true, "is_primitive": true, "is_simple": false, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 12, "label": "2.31.f_co", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 6, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [2, 3], "number_fields": ["2.0.123.1", "2.0.3.1"], "p": 31, "p_rank": 2, "p_rank_deficit": 0, "pic_prime_gens": [[2, 7, 1, 3], [1, 11, 1, 6]], "poly": [1, 5, 66, 155, 961], "poly_str": "1 5 66 155 961 ", "primitive_models": [], "principal_polarization_count": 24, "q": 31, "real_poly": [1, 5, 4], "simple_distinct": ["1.31.b", "1.31.e"], "simple_factors": ["1.31.bA", "1.31.eA"], "simple_multiplicities": [1, 1], "singular_primes": ["3,2*V-2", "2,3*F+5"], "size": 56, "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.15129.1", "splitting_polynomials": [[100, 10, 11, -1, 1]], "twist_count": 12, "twists": [["2.31.af_co", "2.961.ed_gzw", 2], ["2.31.ad_cg", "2.961.ed_gzw", 2], ["2.31.d_cg", "2.961.ed_gzw", 2], ["2.31.ak_bz", "2.29791.apk_fabm", 3], ["2.31.i_cr", "2.29791.apk_fabm", 3], ["2.31.am_cv", "2.887503681.xlc_acklrwc", 6], ["2.31.ai_cr", "2.887503681.xlc_acklrwc", 6], ["2.31.ag_cd", "2.887503681.xlc_acklrwc", 6], ["2.31.g_cd", "2.887503681.xlc_acklrwc", 6], ["2.31.k_bz", "2.887503681.xlc_acklrwc", 6], ["2.31.m_cv", "2.887503681.xlc_acklrwc", 6]], "weak_equivalence_count": 12, "zfv_index": 54, "zfv_index_factorization": [[2, 1], [3, 3]], "zfv_is_bass": false, "zfv_is_maximal": false, "zfv_pic_size": 18, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 13284, "zfv_singular_count": 4, "zfv_singular_primes": ["3,2*V-2", "2,3*F+5"]}