# Stored data for abelian variety isogeny class 2.31.a_abs, downloaded from the LMFDB on 12 September 2026.
{"abvar_count": 918, "abvar_counts": [918, 842724, 887545350, 852867026064, 819628328199078, 787736748306622500, 756943935182892103158, 727426272069103757266944, 699053619999006441936660150, 671790596386415520602800050084], "abvar_counts_str": "918 842724 887545350 852867026064 819628328199078 787736748306622500 756943935182892103158 727426272069103757266944 699053619999006441936660150 671790596386415520602800050084 ", "angle_corank": 1, "angle_rank": 1, "angles": [0.124420346277995, 0.875579653722005], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 32, "curve_counts": [32, 874, 29792, 923494, 28629152, 887587018, 27512614112, 852894731134, 26439622160672, 819628369417354], "curve_counts_str": "32 874 29792 923494 28629152 887587018 27512614112 852894731134 26439622160672 819628369417354 ", "curves": ["y^2=14*x^6+20*x^5+26*x^3+29*x^2+25*x+19", "y^2=11*x^6+29*x^5+16*x^3+25*x^2+13*x+26", "y^2=13*x^6+15*x^5+2*x^4+25*x^3+29*x^2+29*x+2", "y^2=8*x^6+14*x^5+6*x^4+13*x^3+25*x^2+25*x+6", "y^2=28*x^6+16*x^5+4*x^3+20*x^2+17*x+2", "y^2=22*x^6+17*x^5+12*x^3+29*x^2+20*x+6", "y^2=20*x^6+29*x^5+29*x^4+29*x^3+26*x^2+22*x+8", "y^2=29*x^6+25*x^5+25*x^4+25*x^3+16*x^2+4*x+24", "y^2=25*x^6+8*x^5+16*x^4+9*x^3+28*x^2+14*x+16", "y^2=13*x^6+24*x^5+17*x^4+27*x^3+22*x^2+11*x+17", "y^2=15*x^6+17*x^5+4*x^4+2*x^3+23*x^2+27*x+19", "y^2=14*x^6+20*x^5+12*x^4+6*x^3+7*x^2+19*x+26", "y^2=24*x^6+28*x^5+28*x^4+12*x^3+26*x^2+19*x+29", "y^2=10*x^6+22*x^5+22*x^4+5*x^3+16*x^2+26*x+25", "y^2=6*x^6+14*x^5+8*x^4+18*x^3+24*x^2+x+24", "y^2=18*x^6+11*x^5+24*x^4+23*x^3+10*x^2+3*x+10", "y^2=23*x^6+16*x^5+14*x^4+2*x^3+26*x^2+4*x+30", "y^2=7*x^6+17*x^5+11*x^4+6*x^3+16*x^2+12*x+28"], "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": 4, "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": ["2.0.212.1"], "geometric_splitting_field": "2.0.212.1", "geometric_splitting_polynomials": [[53, 0, 1]], "group_structure_count": 2, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 18, "is_cyclic": false, "is_geometrically_simple": false, "is_geometrically_squarefree": false, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 18, "label": "2.31.a_abs", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 8, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [3], "number_fields": ["4.0.719104.2"], "p": 31, "p_rank": 2, "p_rank_deficit": 0, "poly": [1, 0, -44, 0, 961], "poly_str": "1 0 -44 0 961 ", "primitive_models": [], "q": 31, "real_poly": [1, 0, -106], "simple_distinct": ["2.31.a_abs"], "simple_factors": ["2.31.a_absA"], "simple_multiplicities": [1], "singular_primes": ["3,6*F-2*V-2", "3,26*F-21*V-5"], "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.719104.2", "splitting_polynomials": [[729, 0, -52, 0, 1]], "twist_count": 4, "twists": [["2.31.a_bs", "2.923521.abc_ebcpq", 4], ["2.31.ag_s", "2.852891037441.icebc_ynbefxoxq", 8], ["2.31.g_s", "2.852891037441.icebc_ynbefxoxq", 8]], "weak_equivalence_count": 4, "zfv_index": 9, "zfv_index_factorization": [[3, 2]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 324, "zfv_singular_count": 4, "zfv_singular_primes": ["3,6*F-2*V-2", "3,26*F-21*V-5"]}