# Stored data for abelian variety isogeny class 2.31.ae_cf, downloaded from the LMFDB on 20 September 2026.
{"abvar_count": 891, "abvar_counts": [891, 1021977, 894920400, 851741181225, 819538870606731, 787658433931987200, 756937487317157159211, 727423251278723140430025, 699054052572746057253963600, 671790555403053561331832662137], "abvar_counts_str": "891 1021977 894920400 851741181225 819538870606731 787658433931987200 756937487317157159211 727423251278723140430025 699054052572746057253963600 671790555403053561331832662137 ", "angle_corank": 0, "angle_rank": 2, "angles": [0.351775594289712, 0.528623632521575], "center_dim": 4, "cohen_macaulay_max": 2, "curve_count": 28, "curve_counts": [28, 1060, 30040, 922276, 28626028, 887498782, 27512379748, 852891189316, 26439638521480, 819628319414980], "curve_counts_str": "28 1060 30040 922276 28626028 887498782 27512379748 852891189316 26439638521480 819628319414980 ", "curves": ["y^2=23*x^6+20*x^5+26*x^4+17*x^3+25*x^2+17*x+18", "y^2=27*x^6+25*x^5+28*x^4+7*x^3+12*x^2+6*x+26", "y^2=19*x^6+9*x^5+24*x^4+25*x^3+15*x^2+4*x+7", "y^2=26*x^6+23*x^5+6*x^4+19*x^3+3*x^2+2*x+29", "y^2=12*x^6+9*x^5+15*x^4+17*x^3+13*x^2+2*x+13", "y^2=30*x^6+25*x^5+12*x^4+2*x^3+11*x^2+4*x+23", "y^2=28*x^6+30*x^5+25*x^4+28*x^3+4*x^2+3*x+25", "y^2=26*x^6+17*x^5+29*x^4+28*x^3+3*x^2+7*x+30", "y^2=22*x^6+22*x^5+17*x^4+17*x^3+30*x^2+27*x+13", "y^2=30*x^6+10*x^5+5*x^4+9*x^3+18*x^2+23*x+4", "y^2=13*x^6+16*x^5+13*x^4+21*x^3+29*x^2+27*x+26", "y^2=20*x^6+22*x^5+6*x^4+17*x^3+8*x^2+9*x+2", "y^2=26*x^6+25*x^5+14*x^4+22*x^3+15*x^2+10*x+18", "y^2=6*x^6+10*x^5+20*x^4+5*x^3+7*x^2+2*x+6", "y^2=13*x^6+24*x^5+8*x^4+17*x^3+20*x^2+26*x+21", "y^2=28*x^6+4*x^5+10*x^4+13*x^3+15*x^2+27*x+25", "y^2=30*x^6+27*x^5+8*x^4+29*x^3+29*x^2+20*x+28", "y^2=8*x^6+10*x^5+27*x^4+29*x^3+22*x^2+8*x+2", "y^2=27*x^6+26*x^5+22*x^4+8*x^3+21*x^2+30*x+8", "y^2=10*x^6+19*x^5+16*x^4+15*x^3+9*x^2+20*x+7", "y^2=24*x^6+23*x^5+28*x^4+13*x^3+19*x^2+6*x+29", "y^2=9*x^6+29*x^5+21*x^4+4*x^3+23*x^2+26*x+18", "y^2=3*x^6+27*x^5+28*x^4+16*x^3+25*x^2+15*x+24", "y^2=27*x^6+5*x^5+5*x^4+18*x^3+28*x^2+29*x+5", "y^2=19*x^6+16*x^5+16*x^4+2*x^3+17*x^2+24", "y^2=3*x^6+4*x^5+6*x^4+17*x^3+15*x^2+25*x+12", "y^2=22*x^6+25*x^5+x^4+25*x^3+5*x^2+5*x+22", "y^2=6*x^6+x^5+25*x^4+16*x^3+22*x^2+12", "y^2=8*x^6+x^5+26*x^4+x^3+11*x^2+16*x+16", "y^2=5*x^6+4*x^5+25*x^4+26*x^3+23*x^2+27*x+6", "y^2=26*x^6+11*x^5+22*x^4+26*x^3+3*x^2+16*x+26", "y^2=30*x^6+12*x^5+24*x^4+3*x^3+29*x^2+13*x+27", "y^2=8*x^6+22*x^5+20*x^4+26*x^3+21*x^2+30*x+6", "y^2=29*x^6+29*x^5+19*x^4+2*x^3+19*x^2+29*x+29", "y^2=2*x^6+11*x^5+10*x^4+29*x^3+12*x^2+9", "y^2=5*x^6+11*x^5+x^4+9*x^2+23*x+18", "y^2=19*x^6+9*x^5+30*x^4+5*x^3+21*x^2+x+28", "y^2=3*x^6+22*x^5+7*x^4+10*x^3+24*x^2+6*x+23", "y^2=27*x^6+5*x^5+8*x^4+2*x^3+25*x^2+12*x+2", "y^2=6*x^6+18*x^5+8*x^4+x^3+8*x^2+18*x+6", "y^2=8*x^6+23*x^5+15*x^4+7*x^3+15*x^2+23*x+8", "y^2=24*x^6+26*x^5+2*x^4+22*x^3+x^2+3"], "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": 12, "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": ["2.0.11.1", "2.0.123.1"], "geometric_splitting_field": "4.0.1830609.2", "geometric_splitting_polynomials": [[784, 0, 67, 0, 1]], "group_structure_count": 4, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 42, "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": 42, "label": "2.31.ae_cf", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 2, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [3], "number_fields": ["2.0.11.1", "2.0.123.1"], "p": 31, "p_rank": 2, "p_rank_deficit": 0, "poly": [1, -4, 57, -124, 961], "poly_str": "1 -4 57 -124 961 ", "primitive_models": [], "q": 31, "real_poly": [1, -4, -5], "simple_distinct": ["1.31.af", "1.31.b"], "simple_factors": ["1.31.afA", "1.31.bA"], "simple_multiplicities": [1, 1], "singular_primes": ["3,-F^2+F-48", "2,F-V-5"], "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.1830609.2", "splitting_polynomials": [[784, 0, 67, 0, 1]], "twist_count": 4, "twists": [["2.31.ag_cp", "2.961.du_get", 2], ["2.31.e_cf", "2.961.du_get", 2], ["2.31.g_cp", "2.961.du_get", 2]], "weak_equivalence_count": 14, "zfv_index": 108, "zfv_index_factorization": [[2, 2], [3, 3]], "zfv_is_bass": false, "zfv_is_maximal": false, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 12177, "zfv_singular_count": 4, "zfv_singular_primes": ["3,-F^2+F-48", "2,F-V-5"]}