# Stored data for abelian variety isogeny class 2.31.i_bg, downloaded from the LMFDB on 14 May 2026.
{"abvar_count": 1250, "abvar_counts": [1250, 922500, 902161250, 851006250000, 819429281281250, 787662785552602500, 756951099759518161250, 727424490738585600000000, 699053236806744851385601250, 671790528819081737936145562500], "abvar_counts_str": "1250 922500 902161250 851006250000 819429281281250 787662785552602500 756951099759518161250 727424490738585600000000 699053236806744851385601250 671790528819081737936145562500 ", "angle_corank": 1, "angle_rank": 1, "angles": [0.41961520072172, 0.91961520072172], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 40, "curve_counts": [40, 962, 30280, 921478, 28622200, 887503682, 27512874520, 852892642558, 26439607667560, 819628286980802], "curve_counts_str": "40 962 30280 921478 28622200 887503682 27512874520 852892642558 26439607667560 819628286980802 ", "curves": ["y^2=8*x^6+16*x^5+14*x^4+29*x^3+22*x^2+4*x+30", "y^2=16*x^5+29*x^4+30*x^3+23*x^2+3*x+8", "y^2=28*x^6+10*x^5+23*x^4+23*x^2+21*x+28", "y^2=5*x^6+x^5+5*x^4+5*x^3+14*x+10", "y^2=14*x^6+x^5+17*x^4+7*x^3+5*x^2+23*x+18", "y^2=22*x^6+10*x^5+17*x^4+11*x^3+4*x^2+2*x+25", "y^2=7*x^6+21*x^5+30*x^4+7*x^3+25*x^2+17*x+21", "y^2=27*x^6+28*x^5+28*x^4+28*x^2+3*x+27", "y^2=16*x^6+13*x^5+15*x^4+4*x^3+20*x^2+19*x+28", "y^2=8*x^6+10*x^5+23*x^4+4*x^3+x^2+x+19", "y^2=15*x^6+29*x^5+19*x^4+7*x^3+11*x^2+16*x+12", "y^2=7*x^6+6*x^5+17*x^4+17*x^3+2*x^2+4*x+9", "y^2=8*x^6+22*x^5+14*x^4+27*x^3+20*x^2+13*x+5", "y^2=14*x^6+21*x^5+x^4+23*x^3+19*x^2+16*x+25", "y^2=8*x^5+4*x^4+18*x^3+23*x^2+29*x+2", "y^2=16*x^6+9*x^5+29*x^4+x+23", "y^2=8*x^6+12*x^5+27*x^4+2*x^3+24*x^2+2*x+17", "y^2=22*x^6+7*x^5+21*x^4+5*x^2+16*x+20", "y^2=8*x^6+22*x^5+29*x^4+12*x^3+6*x^2+9*x+25", "y^2=18*x^6+30*x^5+3*x^3+4*x^2+5*x+23", "y^2=8*x^6+x^5+27*x^3+24*x^2+18*x+14", "y^2=28*x^6+24*x^5+4*x^4+11*x^3+8*x^2+16*x+23", "y^2=20*x^6+22*x^5+27*x^4+17*x^3+29*x+6", "y^2=12*x^6+25*x^5+10*x^4+4*x^3+10*x^2+30*x+6", "y^2=24*x^6+4*x^5+12*x^4+12*x^3+27*x^2+27*x+16", "y^2=20*x^6+25*x^5+30*x^4+26*x^3+16*x^2+6*x+24"], "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": 4, "geometric_galois_groups": ["2T1"], "geometric_number_fields": ["2.0.184.1"], "geometric_splitting_field": "2.0.184.1", "geometric_splitting_polynomials": [[46, 0, 1]], "group_structure_count": 2, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 26, "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": 26, "label": "2.31.i_bg", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 8, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [5], "number_fields": ["4.0.135424.2"], "p": 31, "p_rank": 2, "p_rank_deficit": 0, "poly": [1, 8, 32, 248, 961], "poly_str": "1 8 32 248 961 ", "primitive_models": [], "q": 31, "real_poly": [1, 8, -30], "simple_distinct": ["2.31.i_bg"], "simple_factors": ["2.31.i_bgA"], "simple_multiplicities": [1], "singular_primes": ["5,10*F+7*V+63", "3,2*F+4*V+33"], "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.135424.2", "splitting_polynomials": [[529, 0, 0, 0, 1]], "twist_count": 4, "twists": [["2.31.ai_bg", "2.961.a_abni", 2], ["2.31.a_abe", "2.852891037441.dnilg_lgowonody", 8], ["2.31.a_be", "2.852891037441.dnilg_lgowonody", 8]], "weak_equivalence_count": 4, "zfv_index": 15, "zfv_index_factorization": [[3, 1], [5, 1]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 900, "zfv_singular_count": 4, "zfv_singular_primes": ["5,10*F+7*V+63", "3,2*F+4*V+33"]}