# Stored data for abelian variety isogeny class 2.31.a_aby, downloaded from the LMFDB on 09 October 2025.
{"abvar_count": 912, "abvar_counts": [912, 831744, 887522832, 851825627136, 819628344225552, 787696777321300224, 756943935236198358672, 727425702527816540160000, 699053619999001074188571792, 671790622657919960542649704704], "abvar_counts_str": "912 831744 887522832 851825627136 819628344225552 787696777321300224 756943935236198358672 727425702527816540160000 699053619999001074188571792 671790622657919960542649704704 ", "angle_corank": 1, "angle_rank": 1, "angles": [0.100692558008054, 0.899307441991946], "center_dim": 4, "cohen_macaulay_max": 3, "curve_count": 32, "curve_counts": [32, 862, 29792, 922366, 28629152, 887541982, 27512614112, 852894063358, 26439622160672, 819628401470302], "curve_counts_str": "32 862 29792 922366 28629152 887541982 27512614112 852894063358 26439622160672 819628401470302 ", "curves": ["y^2=15*x^6+8*x^5+22*x^4+6*x^3+8*x^2+27*x+22", "y^2=x^6+3*x^3+27", "y^2=5*x^6+17*x^5+6*x^4+28*x^3+4*x^2+14*x+18", "y^2=9*x^6+13*x^5+2*x^4+24*x^3+2*x^2+25*x+17", "y^2=2*x^6+3*x^5+21*x^4+29*x^3+2*x^2+17*x", "y^2=29*x^6+13*x^5+29*x^4+19*x^3+5*x^2+25*x+7", "y^2=4*x^6+10*x^5+20*x^4+22*x^3+26*x^2+8*x+21", "y^2=14*x^6+28*x^5+14*x^4+2*x^3+23*x^2+18*x+17", "y^2=x^6+17*x^3+15", "y^2=28*x^6+13*x^5+14*x^4+16*x^3+12*x+28", "y^2=27*x^5+10*x^4+3*x^3+15*x^2+24*x+28", "y^2=22*x^6+29*x^5+11*x^4+17*x^3+28*x^2+6*x+18", "y^2=x^6+12*x^3+23", "y^2=28*x^6+7*x^5+13*x^4+27*x^3+16*x^2+17*x+16", "y^2=12*x^6+23*x^5+5*x^4+24*x^3+6*x^2+17*x+19", "y^2=30*x^6+30*x^5+12*x^4+12*x^3+2*x^2+6*x+1", "y^2=12*x^6+28*x^5+10*x^4+29*x^3+16*x^2+20*x+9", "y^2=5*x^6+22*x^5+30*x^4+25*x^3+17*x^2+29*x+27", "y^2=x^6+22*x^3+15", "y^2=27*x^6+19*x^5+28*x^4+10*x^3+2*x^2+25*x+16", "y^2=16*x^6+8*x^5+8*x^4+13*x^3+29*x+4", "y^2=x^6+x^3+15", "y^2=x^6+x^3+29", "y^2=14*x^6+2*x^5+13*x^4+30*x^3+5*x^2+18*x+18", "y^2=28*x^6+29*x^5+2*x^4+20*x^3+21*x^2+12*x+3", "y^2=20*x^6+20*x^5+16*x^4+14*x^3+21*x^2+2*x+22"], "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": 12, "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": ["2.0.84.1"], "geometric_splitting_field": "2.0.84.1", "geometric_splitting_polynomials": [[21, 0, 1]], "group_structure_count": 5, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 26, "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.a_aby", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 6, "newton_coelevation": 2, "newton_elevation": 0, "number_fields": ["4.0.7056.3"], "p": 31, "p_rank": 2, "p_rank_deficit": 0, "poly": [1, 0, -50, 0, 961], "poly_str": "1 0 -50 0 961 ", "primitive_models": [], "q": 31, "real_poly": [1, 0, -112], "simple_distinct": ["2.31.a_aby"], "simple_factors": ["2.31.a_abyA"], "simple_multiplicities": [1], "singular_primes": ["2,2*F-V-5"], "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.7056.3", "splitting_polynomials": [[49, 0, 7, 0, 1]], "twist_count": 4, "twists": [["2.31.ag_br", "2.29791.a_bcio", 3], ["2.31.g_br", "2.29791.a_bcio", 3], ["2.31.a_by", "2.923521.absm_eucnm", 4], ["2.31.ag_br", "2.887503681.cerc_gygtjlm", 6]], "weak_equivalence_count": 15, "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": 144, "zfv_singular_count": 2, "zfv_singular_primes": ["2,2*F-V-5"]}