# Stored data for abelian variety isogeny class 2.31.a_abi, downloaded from the LMFDB on 09 December 2025.
{"abvar_count": 928, "abvar_counts": [928, 861184, 887562400, 854308306944, 819628273402528, 787767013893760000, 756943935176969972128, 727425271523747393961984, 699053619999091149343069600, 671790506560809188110316790784], "abvar_counts_str": "928 861184 887562400 854308306944 819628273402528 787767013893760000 756943935176969972128 727425271523747393961984 699053619999091149343069600 671790506560809188110316790784 ", "angle_corank": 1, "angle_rank": 1, "angles": [0.15762102420564, 0.84237897579436], "center_dim": 4, "cohen_macaulay_max": 3, "curve_count": 32, "curve_counts": [32, 894, 29792, 925054, 28629152, 887621118, 27512614112, 852893558014, 26439622160672, 819628259824254], "curve_counts_str": "32 894 29792 925054 28629152 887621118 27512614112 852893558014 26439622160672 819628259824254 ", "curves": ["y^2=23*x^6+28*x^5+30*x^4+26*x^3+28*x^2+4*x+1", "y^2=12*x^6+4*x^5+17*x^4+7*x^3+5*x^2+10*x+7", "y^2=26*x^6+25*x^5+18*x^4+7*x^3+10*x^2+18*x+12", "y^2=21*x^6+25*x^5+23*x^4+9*x^3+26*x^2+17*x+3", "y^2=25*x^6+10*x^5+5*x^4+2*x^3+10*x^2+11*x+1", "y^2=13*x^6+27*x^4+15*x^3+x^2+27*x+1", "y^2=8*x^6+19*x^4+14*x^3+3*x^2+19*x+3", "y^2=7*x^6+17*x^5+9*x^4+16*x^3+28*x^2+11*x+24", "y^2=23*x^6+22*x^5+8*x^4+27*x^3+20*x^2+10", "y^2=24*x^6+27*x^5+30*x^4+x^3+x^2+6*x", "y^2=14*x^6+16*x^5+10*x^4+24*x^3+29*x^2+18*x+17", "y^2=23*x^6+6*x^5+18*x^4+12*x^3+12*x^2+4*x+7", "y^2=18*x^6+23*x^5+15*x^4+28*x^2+22*x+13", "y^2=3*x^6+27*x^5+28*x^4+26*x^3+17*x+1", "y^2=9*x^6+19*x^5+22*x^4+16*x^3+20*x+3", "y^2=x^6+22*x^5+x^4+27*x^3+6*x^2+5*x+6", "y^2=30*x^6+10*x^5+5*x^4+26*x^3+15*x^2+10*x+19", "y^2=28*x^6+30*x^5+15*x^4+16*x^3+14*x^2+30*x+26", "y^2=7*x^6+8*x^5+4*x^4+20*x^3+23*x^2+16*x+15", "y^2=30*x^6+11*x^5+18*x^4+8*x^3+2*x^2+19*x", "y^2=5*x^6+20*x^5+24*x^4+30*x^3+24*x^2+29*x+6", "y^2=15*x^6+29*x^5+10*x^4+28*x^3+10*x^2+25*x+18", "y^2=17*x^5+29*x^4+17*x^3+7*x^2+26*x+15", "y^2=22*x^6+26*x^5+16*x^3+12*x+20", "y^2=22*x^6+29*x^5+23*x^4+6*x^3+27*x^2+2*x+27", "y^2=14*x^6+16*x^5+3*x^4+7*x^3+5*x^2+10*x+12", "y^2=11*x^6+20*x^5+x^4+8*x^3+16*x^2+10*x+12", "y^2=21*x^6+9*x^5+23*x^4+29*x^3+28*x^2+25*x+18", "y^2=19*x^6+22*x^5+21*x^4+20*x^3+25*x^2+26*x+8", "y^2=7*x^6+29*x^5+x^4+10*x^3+8*x^2+18*x+13", "y^2=30*x^6+7*x^5+14*x^4+27*x^3+26*x^2+15*x+17", "y^2=25*x^5+3*x^4+27*x^3+9*x^2+8*x", "y^2=29*x^6+30*x^5+21*x^4+22*x^2+29*x+2", "y^2=25*x^6+28*x^5+x^4+4*x^2+25*x+6"], "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": ["2.0.168.1"], "geometric_splitting_field": "2.0.168.1", "geometric_splitting_polynomials": [[42, 0, 1]], "group_structure_count": 6, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 34, "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": 34, "label": "2.31.a_abi", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 4, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [2], "number_fields": ["4.0.28224.4"], "p": 31, "p_rank": 2, "p_rank_deficit": 0, "poly": [1, 0, -34, 0, 961], "poly_str": "1 0 -34 0 961 ", "primitive_models": [], "q": 31, "real_poly": [1, 0, -96], "simple_distinct": ["2.31.a_abi"], "simple_factors": ["2.31.a_abiA"], "simple_multiplicities": [1], "singular_primes": ["2,8*F-7*V-5"], "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.28224.4", "splitting_polynomials": [[58, 8, -7, -2, 1]], "twist_count": 2, "twists": [["2.31.a_bi", "2.923521.cgy_fimhq", 4]], "weak_equivalence_count": 23, "zfv_index": 64, "zfv_index_factorization": [[2, 6]], "zfv_is_bass": false, "zfv_is_maximal": false, "zfv_plus_index": 4, "zfv_plus_index_factorization": [[2, 2]], "zfv_plus_norm": 784, "zfv_singular_count": 2, "zfv_singular_primes": ["2,8*F-7*V-5"]}