# Stored data for abelian variety isogeny class 2.31.af_cg, downloaded from the LMFDB on 15 July 2026.
{"abvar_count": 860, "abvar_counts": [860, 1014800, 895882640, 852143796800, 819588963586500, 787659228711276800, 756934725593164732340, 727422373618116167532800, 699054035897583652206828560, 671790595609587333970514250000], "abvar_counts_str": "860 1014800 895882640 852143796800 819588963586500 787659228711276800 756934725593164732340 727422373618116167532800 699054035897583652206828560 671790595609587333970514250000 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 0, "angle_rank": 2, "angles": [0.328899069140533, 0.520067493920394], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 27, "curve_counts": [27, 1053, 30072, 922713, 28627777, 887499678, 27512279367, 852890160273, 26439637890792, 819628368469573], "curve_counts_str": "27 1053 30072 922713 28627777 887499678 27512279367 852890160273 26439637890792 819628368469573 ", "curves": ["y^2=6*x^5+17*x^4+22*x^3+9*x^2+26*x+27", "y^2=7*x^6+3*x^5+19*x^4+25*x^3+21*x^2+2*x+26", "y^2=4*x^6+5*x^5+23*x^4+2*x^3+x^2+7*x+4", "y^2=13*x^6+17*x^5+29*x^4+20*x^3+8*x^2+25*x+25", "y^2=16*x^6+12*x^5+23*x^4+18*x^3+16*x^2+18*x+3", "y^2=21*x^6+29*x^5+17*x^4+6*x^3+27*x^2+3", "y^2=14*x^6+18*x^5+13*x^4+30*x^3+19*x^2+22*x+19", "y^2=10*x^6+21*x^5+16*x^4+24*x^3+5*x^2+18*x+9", "y^2=3*x^5+18*x^4+19*x^3+3*x^2+16*x+7", "y^2=7*x^6+7*x^5+6*x^4+7*x^3+26*x^2+16*x+20", "y^2=22*x^6+16*x^5+4*x^4+x^3+23*x^2+5*x", "y^2=6*x^6+29*x^5+26*x^4+2*x^3+21*x^2+22*x+29", "y^2=29*x^6+26*x^5+18*x^4+3*x^3+8*x^2+6*x+15", "y^2=20*x^6+17*x^5+3*x^4+19*x^3+23*x^2+24*x+4", "y^2=14*x^6+28*x^5+12*x^4+23*x^3+14*x^2+19", "y^2=6*x^6+9*x^5+17*x^4+14*x^3+13*x^2+11*x+17", "y^2=3*x^6+7*x^5+20*x^4+11*x^3+26*x^2+23*x+19", "y^2=10*x^6+9*x^5+14*x^4+26*x^3+19*x^2+22*x+27", "y^2=30*x^6+9*x^5+23*x^4+12*x^3+14*x^2+24*x+4", "y^2=5*x^6+29*x^5+8*x^4+11*x^3+11*x^2+19*x", "y^2=10*x^6+29*x^5+15*x^4+5*x^3+24*x^2+13*x+11", "y^2=12*x^6+12*x^5+11*x^4+18*x^3+12*x^2+30*x+6", "y^2=29*x^6+11*x^5+19*x^3+8*x^2+6*x+17", "y^2=10*x^6+10*x^5+26*x^4+24*x^3+26*x^2+29*x+23", "y^2=15*x^6+28*x^5+5*x^4+10*x^3+27*x^2+7*x", "y^2=11*x^6+10*x^5+x^4+26*x^3+17*x^2+11*x+14", "y^2=19*x^6+10*x^5+13*x^4+22*x^3+14*x^2+22*x+29", "y^2=15*x^6+12*x^5+11*x^4+2*x^3+16*x^2+15*x", "y^2=30*x^6+14*x^5+10*x^4+19*x^3+19*x^2+20*x+5", "y^2=24*x^6+20*x^5+2*x^4+18*x^3+14*x^2+6", "y^2=17*x^6+20*x^5+3*x^4+8*x^3+24*x^2+22*x+15", "y^2=30*x^6+17*x^5+20*x^4+22*x^3+7*x^2+3*x+29"], "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": 2, "g": 2, "galois_groups": ["4T3"], "geom_dim1_distinct": 0, "geom_dim1_factors": 0, "geom_dim2_distinct": 1, "geom_dim2_factors": 1, "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": ["4T3"], "geometric_number_fields": ["4.0.4748825.1"], "geometric_splitting_field": "4.0.4748825.1", "geometric_splitting_polynomials": [[860, -50, 49, -1, 1]], "group_structure_count": 2, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 32, "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": 32, "label": "2.31.af_cg", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 2, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [2], "number_fields": ["4.0.4748825.1"], "p": 31, "p_rank": 2, "p_rank_deficit": 0, "pic_prime_gens": [[1, 5, 1, 2], [1, 5, 2, 2], [1, 23, 1, 4], [1, 31, 1, 12]], "poly": [1, -5, 58, -155, 961], "poly_str": "1 -5 58 -155 961 ", "primitive_models": [], "principal_polarization_count": 32, "q": 31, "real_poly": [1, -5, -4], "simple_distinct": ["2.31.af_cg"], "simple_factors": ["2.31.af_cgA"], "simple_multiplicities": [1], "singular_primes": ["2,-2*F^2-V+3"], "size": 32, "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.4748825.1", "splitting_polynomials": [[860, -50, 49, -1, 1]], "twist_count": 2, "twists": [["2.31.f_cg", "2.961.dn_fns", 2]], "weak_equivalence_count": 2, "zfv_index": 2, "zfv_index_factorization": [[2, 1]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_pic_size": 24, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 11300, "zfv_singular_count": 2, "zfv_singular_primes": ["2,-2*F^2-V+3"]}