# Stored data for abelian variety isogeny class 2.31.a_abu, downloaded from the LMFDB on 29 September 2025.
{"abvar_count": 916, "abvar_counts": [916, 839056, 887538964, 852534595584, 819628336307476, 787725412618193296, 756943935197782027156, 727426208204485983535104, 699053619998995019546996884, 671790609678160980574413490576], "abvar_counts_str": "916 839056 887538964 852534595584 819628336307476 787725412618193296 756943935197782027156 727426208204485983535104 699053619998995019546996884 671790609678160980574413490576 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 1, "angle_rank": 1, "angles": [0.116954024640961, 0.883045975359039], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 32, "curve_counts": [32, 870, 29792, 923134, 28629152, 887574246, 27512614112, 852894656254, 26439622160672, 819628385634150], "curve_counts_str": "32 870 29792 923134 28629152 887574246 27512614112 852894656254 26439622160672 819628385634150 ", "curves": ["y^2=16*x^6+17*x^5+11*x^4+22*x^2+25*x+4", "y^2=3*x^6+5*x^5+17*x^4+22*x^3+18*x^2+7*x+7", "y^2=5*x^6+11*x^5+25*x^4+21*x^3+22*x^2+17*x+13", "y^2=9*x^6+24*x^5+23*x^4+7*x^3+8*x^2+24*x+22", "y^2=13*x^6+23*x^5+22*x^4+22*x^3+20*x^2+29*x+10", "y^2=9*x^6+25*x^5+7*x^4+22*x^3+15*x^2+26*x+22", "y^2=27*x^6+13*x^5+21*x^4+4*x^3+14*x^2+16*x+4", "y^2=30*x^6+13*x^5+30*x^4+22*x^3+25*x^2+3*x+1", "y^2=24*x^6+5*x^5+23*x^4+29*x^3+5*x^2+x+15", "y^2=28*x^6+14*x^5+21*x^4+5*x^3+9*x^2+23*x+24", "y^2=21*x^6+12*x^5+17*x^4+13*x^2+8*x+13", "y^2=28*x^6+26*x^5+12*x^4+24*x^3+7*x^2+11*x+24", "y^2=x^6+30*x^5+23*x^4+18*x^3+25*x^2+13*x+29", "y^2=15*x^6+23*x^5+23*x^4+12*x^2+18*x+23", "y^2=10*x^6+29*x^5+19*x^4+20*x^3+17*x^2+28*x+7", "y^2=30*x^6+25*x^5+26*x^4+29*x^3+20*x^2+22*x+21", "y^2=19*x^6+2*x^5+x^4+29*x^3+30*x^2+10*x+6", "y^2=26*x^6+6*x^5+3*x^4+25*x^3+28*x^2+30*x+18", "y^2=12*x^5+17*x^4+28*x^3+4*x^2+13*x", "y^2=24*x^6+7*x^5+15*x^4+20*x^3+11*x^2+21*x+18", "y^2=10*x^6+21*x^5+14*x^4+29*x^3+2*x^2+x+23", "y^2=28*x^6+22*x^5+26*x^4+20*x^2+11*x+6", "y^2=12*x^6+3*x^5+27*x^3+6*x+25", "y^2=16*x^6+30*x^5+27*x^4+18*x^3+21*x^2+5*x+2", "y^2=15*x^6+23*x^5+23*x^4+15*x^3+8*x^2+23*x+16", "y^2=5*x^6+28*x^5+8*x^4+3*x^3+19*x^2+2*x+28", "y^2=15*x^6+22*x^5+24*x^4+9*x^3+26*x^2+6*x+22", "y^2=9*x^5+2*x^4+9*x^3+15*x^2+18*x", "y^2=x^6+x^5+4*x^4+16*x^3+8*x^2+20*x+30", "y^2=17*x^6+6*x^5+22*x^4+26*x^3+14*x^2+6*x+23", "y^2=20*x^6+18*x^5+4*x^4+16*x^3+11*x^2+18*x+7", "y^2=19*x^6+23*x^5+30*x^4+9*x^3+4*x^2+27*x+24", "y^2=7*x^6+23*x^5+26*x^4+28*x^3+2*x^2+26*x+6", "y^2=x^6+9*x^5+24*x^4+19*x^3+20*x^2+14*x+30", "y^2=x^6+16*x^5+14*x^4+26*x^3+17*x^2+16*x+30", "y^2=8*x^6+9*x^5+27*x^4+14*x^3+9*x^2+22*x+26", "y^2=24*x^6+27*x^5+19*x^4+11*x^3+27*x^2+4*x+16", "y^2=20*x^6+6*x^5+23*x^4+27*x^3+25*x^2+x+15", "y^2=12*x^6+23*x^5+29*x^4+2*x^3+24*x^2+29*x+27", "y^2=5*x^6+7*x^5+25*x^4+6*x^3+10*x^2+25*x+19"], "dim1_distinct": 0, "dim1_factors": 0, "dim2_distinct": 1, "dim2_factors": 1, "dim3_distinct": 0, "dim3_factors": 0, "dim4_distinct": 0, "dim4_factors": 0, "dim5_distinct": 0, "dim5_factors": 0, "endomorphism_ring_count": 14, "g": 2, "galois_groups": ["4T2"], "geom_dim1_distinct": 1, "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": 2, "geometric_extension_degree": 2, "geometric_galois_groups": ["2T1"], "geometric_number_fields": ["2.0.3.1"], "geometric_splitting_field": "2.0.3.1", "geometric_splitting_polynomials": [[1, -1, 1]], "group_structure_count": 2, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 40, "is_geometrically_simple": false, "is_geometrically_squarefree": false, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 40, "label": "2.31.a_abu", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 12, "newton_coelevation": 2, "newton_elevation": 0, "number_fields": ["4.0.144.1"], "p": 31, "p_rank": 2, "p_rank_deficit": 0, "pic_prime_gens": [[1, 13, 1, 12]], "poly": [1, 0, -46, 0, 961], "poly_str": "1 0 -46 0 961 ", "primitive_models": [], "principal_polarization_count": 58, "q": 31, "real_poly": [1, 0, -108], "simple_distinct": ["2.31.a_abu"], "simple_factors": ["2.31.a_abuA"], "simple_multiplicities": [1], "singular_primes": ["2,F+1", "3,5*F^2+3*F+5"], "size": 46, "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.144.1", "splitting_polynomials": [[1, 0, -1, 0, 1]], "twist_count": 24, "twists": [["2.31.a_an", "2.29791.a_cafa", 3], ["2.31.a_ch", "2.29791.a_cafa", 3], ["2.31.ai_da", "2.923521.aoy_edfzq", 4], ["2.31.a_bu", "2.923521.aoy_edfzq", 4], ["2.31.i_da", "2.923521.aoy_edfzq", 4], ["2.31.aw_hb", "2.787662783788549761.dlgkxbw_tluogrckpisug", 12], ["2.31.as_fj", "2.787662783788549761.dlgkxbw_tluogrckpisug", 12], ["2.31.ap_ec", "2.787662783788549761.dlgkxbw_tluogrckpisug", 12], ["2.31.ao_eh", "2.787662783788549761.dlgkxbw_tluogrckpisug", 12], ["2.31.al_dm", "2.787662783788549761.dlgkxbw_tluogrckpisug", 12], ["2.31.ah_s", "2.787662783788549761.dlgkxbw_tluogrckpisug", 12], ["2.31.ae_ap", "2.787662783788549761.dlgkxbw_tluogrckpisug", 12], ["2.31.ad_bi", "2.787662783788549761.dlgkxbw_tluogrckpisug", 12], ["2.31.a_ach", "2.787662783788549761.dlgkxbw_tluogrckpisug", 12], ["2.31.a_n", "2.787662783788549761.dlgkxbw_tluogrckpisug", 12], ["2.31.d_bi", "2.787662783788549761.dlgkxbw_tluogrckpisug", 12], ["2.31.e_ap", "2.787662783788549761.dlgkxbw_tluogrckpisug", 12], ["2.31.h_s", "2.787662783788549761.dlgkxbw_tluogrckpisug", 12], ["2.31.l_dm", "2.787662783788549761.dlgkxbw_tluogrckpisug", 12], ["2.31.o_eh", "2.787662783788549761.dlgkxbw_tluogrckpisug", 12], ["2.31.p_ec", "2.787662783788549761.dlgkxbw_tluogrckpisug", 12], ["2.31.s_fj", "2.787662783788549761.dlgkxbw_tluogrckpisug", 12], ["2.31.w_hb", "2.787662783788549761.dlgkxbw_tluogrckpisug", 12]], "weak_equivalence_count": 14, "zfv_index": 576, "zfv_index_factorization": [[2, 6], [3, 2]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_pic_size": 12, "zfv_plus_index": 6, "zfv_plus_index_factorization": [[2, 1], [3, 1]], "zfv_plus_norm": 256, "zfv_singular_count": 4, "zfv_singular_primes": ["2,F+1", "3,5*F^2+3*F+5"]}