# Stored data for abelian variety isogeny class 2.31.a_au, downloaded from the LMFDB on 10 September 2025.
{"abvar_count": 942, "abvar_counts": [942, 887364, 887553342, 855706401936, 819628229868702, 787750934895368964, 756943935261858883662, 727422320983362624000000, 699053619999035285541470862, 671790435197701805332159164804], "abvar_counts_str": "942 887364 887553342 855706401936 819628229868702 787750934895368964 756943935261858883662 727422320983362624000000 699053619999035285541470862 671790435197701805332159164804 ", "angle_corank": 1, "angle_rank": 1, "angles": [0.197724823975034, 0.802275176024967], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 32, "curve_counts": [32, 922, 29792, 926566, 28629152, 887603002, 27512614112, 852890098558, 26439622160672, 819628172756602], "curve_counts_str": "32 922 29792 926566 28629152 887603002 27512614112 852890098558 26439622160672 819628172756602 ", "curves": ["y^2=18*x^6+29*x^5+9*x^4+3*x^3+24*x^2+17*x+18", "y^2=23*x^6+25*x^5+27*x^4+9*x^3+10*x^2+20*x+23", "y^2=2*x^6+17*x^5+2*x^4+8*x^3+7*x^2+3*x+15", "y^2=6*x^6+20*x^5+6*x^4+24*x^3+21*x^2+9*x+14", "y^2=30*x^6+22*x^5+25*x^4+26*x^3+4*x^2+24*x+13", "y^2=28*x^6+4*x^5+13*x^4+16*x^3+12*x^2+10*x+8", "y^2=17*x^6+13*x^5+8*x^4+28*x^3+28*x^2+13*x+17", "y^2=20*x^6+8*x^5+24*x^4+22*x^3+22*x^2+8*x+20", "y^2=20*x^6+12*x^5+6*x^4+25*x^3+11*x^2+5*x+1", "y^2=29*x^6+5*x^5+18*x^4+13*x^3+2*x^2+15*x+3", "y^2=3*x^6+14*x^5+21*x^4+29*x^3+21*x^2+11*x+21", "y^2=9*x^6+11*x^5+x^4+25*x^3+x^2+2*x+1", "y^2=14*x^6+16*x^5+27*x^4+18*x^3+14*x^2+21*x+10", "y^2=11*x^6+17*x^5+19*x^4+23*x^3+11*x^2+x+30", "y^2=21*x^6+15*x^5+14*x^4+27*x^3+7*x^2+4*x+18", "y^2=x^6+14*x^5+11*x^4+19*x^3+21*x^2+12*x+23", "y^2=2*x^6+12*x^5+23*x^4+27*x^3+4*x^2+2*x+28", "y^2=6*x^6+5*x^5+7*x^4+19*x^3+12*x^2+6*x+22", "y^2=x^6+23*x^5+24*x^4+9*x^3+2*x^2+11*x+13", "y^2=3*x^6+7*x^5+10*x^4+27*x^3+6*x^2+2*x+8", "y^2=25*x^6+9*x^5+2*x^4+24*x^3+27*x^2+4*x+24", "y^2=13*x^6+27*x^5+6*x^4+10*x^3+19*x^2+12*x+10", "y^2=3*x^6+13*x^5+9*x^4+14*x^3+10*x^2+2*x+16", "y^2=9*x^6+8*x^5+27*x^4+11*x^3+30*x^2+6*x+17", "y^2=x^6+14*x^5+19*x^4+7*x^3+28*x^2+15*x", "y^2=3*x^6+11*x^5+26*x^4+21*x^3+22*x^2+14*x", "y^2=18*x^6+16*x^5+26*x^4+8*x^3+9*x^2+25*x+26", "y^2=23*x^6+17*x^5+16*x^4+24*x^3+27*x^2+13*x+16", "y^2=7*x^6+3*x^5+22*x^4+5*x^3+13*x^2+12*x+16", "y^2=21*x^6+9*x^5+4*x^4+15*x^3+8*x^2+5*x+17", "y^2=13*x^6+6*x^5+14*x^4+23*x^3+18*x^2+12*x+20", "y^2=8*x^6+18*x^5+11*x^4+7*x^3+23*x^2+5*x+29", "y^2=27*x^6+20*x^5+13*x^4+11*x^3+19*x^2+12*x+16", "y^2=19*x^6+29*x^5+8*x^4+2*x^3+26*x^2+5*x+17", "y^2=15*x^6+27*x^5+12*x^4+27*x^3+14*x^2+24*x+21", "y^2=14*x^6+19*x^5+5*x^4+19*x^3+11*x^2+10*x+1"], "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": 1, "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": ["2.0.3444.1"], "geometric_splitting_field": "2.0.3444.1", "geometric_splitting_polynomials": [[861, 0, 1]], "group_structure_count": 1, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 36, "is_geometrically_simple": false, "is_geometrically_squarefree": false, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 36, "label": "2.31.a_au", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 4, "newton_coelevation": 2, "newton_elevation": 0, "number_fields": ["4.0.189778176.2"], "p": 31, "p_rank": 2, "p_rank_deficit": 0, "poly": [1, 0, -20, 0, 961], "poly_str": "1 0 -20 0 961 ", "primitive_models": [], "q": 31, "real_poly": [1, 0, -82], "simple_distinct": ["2.31.a_au"], "simple_factors": ["2.31.a_auA"], "simple_multiplicities": [1], "singular_primes": [], "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.189778176.2", "splitting_polynomials": [[961, 0, -20, 0, 1]], "twist_count": 2, "twists": [["2.31.a_u", "2.923521.enc_jcxbq", 4]], "weak_equivalence_count": 1, "zfv_index": 1, "zfv_index_factorization": [], "zfv_is_bass": true, "zfv_is_maximal": true, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 1764, "zfv_singular_count": 0, "zfv_singular_primes": []}