# Stored data for abelian variety isogeny class 2.31.c_as, downloaded from the LMFDB on 15 October 2026.
{"abvar_count": 1008, "abvar_counts": [1008, 887040, 896576688, 855106560000, 819662699823408, 787716426600956160, 756929133062679186288, 727422939974376898560000, 699053245601458750869364848, 671790528621553421765605536000], "abvar_counts_str": "1008 887040 896576688 855106560000 819662699823408 787716426600956160 756929133062679186288 727422939974376898560000 699053245601458750869364848 671790528621553421765605536000 ", "angle_corank": 0, "angle_rank": 2, "angles": [0.244865078763254, 0.854999228987298], "center_dim": 4, "cohen_macaulay_max": 2, "curve_count": 34, "curve_counts": [34, 922, 30094, 925918, 28630354, 887564122, 27512076094, 852890824318, 26439608000194, 819628286739802], "curve_counts_str": "34 922 30094 925918 28630354 887564122 27512076094 852890824318 26439608000194 819628286739802 ", "curves": ["y^2=10*x^6+15*x^5+18*x^4+8*x^3+25*x^2+25*x", "y^2=4*x^5+25*x^4+6*x^3+24*x^2+23*x+15", "y^2=2*x^6+11*x^5+3*x^4+20*x^3+26*x^2+3*x+16", "y^2=26*x^6+9*x^5+6*x^4+15*x^3+22*x^2+30*x+20", "y^2=21*x^6+23*x^5+26*x^4+17*x^3+29*x^2+x+18", "y^2=5*x^6+28*x^5+26*x^4+10*x^3+7*x^2+18*x+25", "y^2=19*x^6+25*x^5+14*x^4+22*x^3+5*x^2+x+11", "y^2=6*x^6+22*x^5+13*x^4+2*x^3+22*x^2+14*x+17", "y^2=28*x^6+24*x^5+2*x^4+6*x^3+29*x^2+19*x+27", "y^2=7*x^6+22*x^4+13*x^3+21*x^2+30*x+18", "y^2=23*x^6+x^5+10*x^4+17*x^3+24*x^2+7*x+23", "y^2=7*x^6+28*x^5+6*x^4+x^3+5*x^2+14*x+18", "y^2=7*x^6+10*x^5+17*x^4+5*x^3+30*x^2+9*x+13", "y^2=25*x^6+2*x^5+21*x^4+15*x^3+29*x^2+2*x+9", "y^2=28*x^6+25*x^5+28*x^3+11*x^2+18*x+24", "y^2=30*x^6+13*x^5+19*x^4+2*x^2+15*x+30", "y^2=11*x^6+5*x^5+3*x^4+15*x^3+12*x^2+12*x+29", "y^2=9*x^6+8*x^5+12*x^4+24*x^3+2*x^2+15*x+16", "y^2=12*x^6+17*x^5+24*x^4+24*x^3+24*x^2+17*x+12", "y^2=17*x^6+17*x^5+23*x^4+25*x^3+12*x^2+27*x", "y^2=18*x^5+21*x^4+2*x^3+x^2+5*x+29", "y^2=24*x^6+6*x^5+7*x^4+5*x^3+10*x^2+21*x+17", "y^2=22*x^6+18*x^5+27*x^4+6*x^3+5*x^2+27*x+5", "y^2=22*x^6+27*x^5+4*x^4+26*x^3+10*x^2+28*x+14", "y^2=2*x^6+16*x^5+3*x^4+24*x^3+21*x^2+9*x+11", "y^2=28*x^6+4*x^5+8*x^4+4*x^3+14*x^2+7*x", "y^2=19*x^6+27*x^5+29*x^4+20*x^3+23*x^2+16*x+22", "y^2=30*x^6+26*x^5+5*x^4+13*x^3+25*x^2+20*x+6", "y^2=24*x^6+3*x^5+16*x^4+26*x^3+28*x^2+30*x+13", "y^2=25*x^6+12*x^5+6*x^4+28*x^3+15*x^2+13*x+7", "y^2=16*x^6+25*x^5+23*x^4+22*x^3+x^2+20*x+23", "y^2=13*x^6+5*x^5+23*x^4+23*x^3+3*x^2+2*x+18", "y^2=12*x^6+19*x^5+15*x^4+11*x^3+24*x^2+3*x+17", "y^2=4*x^6+9*x^5+3*x^4+3*x^3+27*x^2+13*x+2", "y^2=18*x^6+25*x^5+24*x^4+16*x^3+4*x^2+8*x+22", "y^2=17*x^6+12*x^5+14*x^4+16*x^3+29*x^2+17", "y^2=5*x^6+2*x^5+26*x^4+6*x^3+3*x^2+x+23", "y^2=10*x^6+2*x^5+19*x^4+15*x^3+13*x^2+23*x+13", "y^2=20*x^6+16*x^5+12*x^4+2*x^3+22*x^2+18*x+16", "y^2=6*x^6+15*x^5+9*x^4+7*x^2+22*x", "y^2=6*x^6+2*x^5+29*x^4+13*x^3+29*x^2+2*x+6", "y^2=16*x^6+5*x^5+24*x^4+27*x^3+27*x^2+3*x+21", "y^2=25*x^6+30*x^5+13*x^4+25*x^3+27*x^2+26*x+22", "y^2=23*x^6+22*x^5+14*x^4+8*x^3+9*x^2+11*x+15", "y^2=28*x^6+2*x^5+7*x^4+27*x^3+13*x^2+4*x", "y^2=14*x^6+17*x^5+20*x^4+16*x^3+22*x^2+14*x+9", "y^2=10*x^5+8*x^4+23*x^3+26*x^2+22", "y^2=25*x^6+19*x^5+18*x^4+9*x^3+25*x^2+5*x+14", "y^2=8*x^6+4*x^5+25*x^4+11*x^3+7*x^2+20*x+16", "y^2=21*x^6+5*x^5+14*x^4+3*x^3+13*x^2+17*x+22", "y^2=13*x^6+11*x^5+13*x^4+25*x^3+16*x^2+12*x+4", "y^2=6*x^6+7*x^5+4*x^4+22*x^3+15*x^2+27*x+25", "y^2=5*x^6+25*x^5+21*x^4+28*x^3+8*x^2+5*x+28", "y^2=13*x^5+21*x^4+15*x^3+18*x^2+10*x+28", "y^2=28*x^6+3*x^5+10*x^4+22*x^3+28*x^2+8*x+25", "y^2=20*x^6+7*x^5+5*x^4+30*x^3+2*x^2+x+6", "y^2=16*x^6+19*x^5+22*x^3+10*x^2+23*x+15", "y^2=18*x^6+17*x^5+29*x^4+22*x^3+27*x^2+19", "y^2=7*x^6+11*x^5+12*x^4+6*x^3+12*x^2+2*x+22", "y^2=8*x^6+16*x^5+29*x^3+27*x^2+15*x+9", "y^2=19*x^6+27*x^5+24*x^4+8*x^3+3*x^2+9*x+15", "y^2=9*x^6+28*x^5+20*x^4+12*x^3+3*x^2+5*x+21", "y^2=8*x^5+28*x^4+25*x^3+2*x^2+4*x+4", "y^2=24*x^6+14*x^5+14*x^4+12*x^3+14*x^2+14*x+24", "y^2=28*x^6+27*x^5+5*x^4+21*x^3+2*x^2+6*x+17", "y^2=21*x^5+20*x^4+27*x^3+27*x^2+3*x+22", "y^2=18*x^6+16*x^5+6*x^4+7*x^3+29*x^2+12*x", "y^2=6*x^6+26*x^5+2*x^4+23*x^3+20*x^2+29*x+23", "y^2=28*x^6+4*x^5+11*x^4+16*x^3+9*x^2+13*x+13", "y^2=5*x^6+2*x^5+3*x^4+23*x^3+23*x^2+15*x+26", "y^2=9*x^6+27*x^5+24*x^4+9*x^3+24*x^2+12*x+13", "y^2=28*x^6+16*x^5+17*x^4+22*x^3+23*x^2+3*x+28", "y^2=9*x^6+x^5+3*x^4+28*x^3+21*x^2+12*x+6", "y^2=7*x^6+4*x^5+22*x^4+7*x^3+3*x^2+7*x+25", "y^2=4*x^6+20*x^5+9*x^4+20*x^3+5*x^2+20*x+25", "y^2=11*x^6+14*x^5+6*x^4+30*x^3+16*x^2+18*x+29", "y^2=8*x^6+29*x^5+16*x^4+16*x^3+16*x^2+9*x+5", "y^2=28*x^6+21*x^5+15*x^4+21*x^3+8*x^2+18*x+6", "y^2=4*x^6+8*x^5+6*x^4+28*x^3+14*x^2+12*x+14", "y^2=19*x^6+27*x^5+x^4+13*x^3+16*x^2+21*x+9", "y^2=10*x^6+9*x^5+16*x^4+26*x^3+27*x^2+18*x+16", "y^2=12*x^6+13*x^5+9*x^4+24*x^3+30*x^2+6*x+30", "y^2=30*x^6+24*x^5+30*x^4+5*x^3+13*x^2+7*x+6", "y^2=30*x^6+26*x^5+2*x^4+26*x^3+29*x^2+18*x+29", "y^2=19*x^6+28*x^5+29*x^4+15*x^3+17*x^2+29*x+22", "y^2=22*x^6+8*x^5+19*x^4+26*x^3+27*x^2+2*x+29", "y^2=28*x^6+15*x^5+6*x^4+11*x^3+6*x^2+15*x+28", "y^2=7*x^6+3*x^5+24*x^4+x^3+20*x^2+16*x+27", "y^2=9*x^6+20*x^5+12*x^4+24*x^3+30*x^2+21*x+19", "y^2=18*x^6+28*x^5+4*x^4+7*x^3+23*x^2+7*x", "y^2=10*x^6+15*x^5+11*x^4+4*x^3+27*x+13", "y^2=4*x^6+4*x^5+24*x^4+26*x^3+21*x^2+24*x+5", "y^2=30*x^6+9*x^5+12*x^4+19*x^3+11*x^2+4*x+29", "y^2=26*x^6+27*x^5+20*x^4+5*x^3+7*x^2+24*x+21", "y^2=26*x^6+4*x^5+25*x^4+30*x^3+23*x^2+28*x+19", "y^2=5*x^6+8*x^5+29*x^4+13*x^3+11*x^2+29*x+7", "y^2=21*x^6+28*x^5+29*x^4+28*x^3+15*x^2+2*x+1", "y^2=5*x^6+17*x^5+15*x^4+x^3+14*x^2+24*x+19", "y^2=7*x^6+x^5+11*x^4+20*x^3+x^2+28*x+18", "y^2=24*x^6+25*x^5+25*x^4+11*x^3+20*x^2+12*x+6", "y^2=29*x^6+14*x^5+18*x^4+4*x^2+16*x+11", "y^2=4*x^6+7*x^5+19*x^4+23*x^3+26*x^2+28*x+17", "y^2=4*x^6+14*x^5+11*x^4+7*x^3+11*x^2+14*x+4", "y^2=27*x^6+12*x^5+26*x^4+6*x^3+20*x^2+7*x+24"], "dim1_distinct": 2, "dim1_factors": 2, "dim2_distinct": 0, "dim2_factors": 0, "dim3_distinct": 0, "dim3_factors": 0, "dim4_distinct": 0, "dim4_factors": 0, "dim5_distinct": 0, "dim5_factors": 0, "endomorphism_ring_count": 30, "g": 2, "galois_groups": ["2T1", "2T1"], "geom_dim1_distinct": 2, "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": 4, "geometric_extension_degree": 1, "geometric_galois_groups": ["2T1", "2T1"], "geometric_number_fields": ["2.0.15.1", "2.0.24.1"], "geometric_splitting_field": "4.0.14400.3", "geometric_splitting_polynomials": [[16, 0, -2, 0, 1]], "group_structure_count": 8, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 104, "is_cyclic": false, "is_geometrically_simple": false, "is_geometrically_squarefree": true, "is_primitive": true, "is_simple": false, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 104, "label": "2.31.c_as", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 2, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [2, 3], "number_fields": ["2.0.15.1", "2.0.24.1"], "p": 31, "p_rank": 2, "p_rank_deficit": 0, "poly": [1, 2, -18, 62, 961], "poly_str": "1 2 -18 62 961 ", "primitive_models": [], "q": 31, "real_poly": [1, 2, -80], "simple_distinct": ["1.31.ai", "1.31.k"], "simple_factors": ["1.31.aiA", "1.31.kA"], "simple_multiplicities": [1, 1], "singular_primes": ["2,-V-9", "3,-F-2*V"], "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.14400.3", "splitting_polynomials": [[16, 0, -2, 0, 1]], "twist_count": 4, "twists": [["2.31.as_fm", "2.961.abo_cyw", 2], ["2.31.ac_as", "2.961.abo_cyw", 2], ["2.31.s_fm", "2.961.abo_cyw", 2]], "weak_equivalence_count": 35, "zfv_index": 648, "zfv_index_factorization": [[2, 3], [3, 4]], "zfv_is_bass": false, "zfv_is_maximal": false, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 1440, "zfv_singular_count": 4, "zfv_singular_primes": ["2,-V-9", "3,-F-2*V"]}