# Stored data for abelian variety isogeny class 2.31.i_bu, downloaded from the LMFDB on 14 May 2026.
{"abvar_count": 1264, "abvar_counts": [1264, 950528, 892092016, 852296634368, 819156831743344, 787748694587379968, 756943852214544396784, 727423356678786146435072, 699053349238967219273354224, 671790509952706128947569406208], "abvar_counts_str": "1264 950528 892092016 852296634368 819156831743344 787748694587379968 756943852214544396784 727423356678786146435072 699053349238967219273354224 671790509952706128947569406208 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 0, "angle_rank": 2, "angles": [0.452462187559062, 0.834089736007715], "center_dim": 4, "cohen_macaulay_max": 3, "curve_count": 40, "curve_counts": [40, 990, 29944, 922878, 28612680, 887600478, 27512611096, 852891312894, 26439611919976, 819628263962590], "curve_counts_str": "40 990 29944 922878 28612680 887600478 27512611096 852891312894 26439611919976 819628263962590 ", "curves": ["y^2=19*x^5+x^4+27*x^3+17*x^2+11*x+13", "y^2=14*x^6+4*x^5+16*x^4+14*x^3+6*x^2+12*x+6", "y^2=12*x^6+4*x^5+21*x^4+2*x^3+19*x^2+18*x+13", "y^2=16*x^6+12*x^5+15*x^4+27*x^3+20*x^2+4*x", "y^2=30*x^6+13*x^5+12*x^3+4*x^2+9*x+7", "y^2=x^6+17*x^5+21*x^4+2*x^3+30*x^2+12*x+12", "y^2=10*x^6+9*x^5+20*x^3+27*x^2+29*x+4", "y^2=4*x^6+26*x^5+27*x^4+24*x^3+20*x^2+29*x+17", "y^2=3*x^6+11*x^5+4*x^4+19*x^3+17*x^2+26*x+2", "y^2=9*x^6+4*x^5+7*x^4+14*x^3+3*x^2+18*x+11", "y^2=2*x^6+26*x^5+5*x^4+30*x^3+30*x^2+18*x+6", "y^2=7*x^6+13*x^5+24*x^4+19*x^3+24*x^2+13*x+20", "y^2=19*x^6+11*x^5+20*x^4+9*x^3+21*x^2+20*x+9", "y^2=x^6+27*x^5+23*x^4+18*x^3+28*x^2+6*x+5", "y^2=19*x^6+13*x^5+21*x^4+21*x^3+14*x^2+2*x+3", "y^2=10*x^6+5*x^5+16*x^4+7*x^3+23*x^2+15*x+25", "y^2=17*x^6+11*x^4+28*x^3+13*x^2+14*x+29", "y^2=22*x^6+17*x^5+4*x^3+2*x^2+18*x", "y^2=14*x^5+12*x^4+22*x^3+16*x^2+24*x+15", "y^2=21*x^6+28*x^5+30*x^3+22*x^2+x+10", "y^2=11*x^6+19*x^5+24*x^4+22*x^3+21*x^2+x+26", "y^2=12*x^6+21*x^5+21*x^4+20*x^3+28*x^2+6*x+14", "y^2=5*x^6+8*x^5+8*x^4+21*x^3+11*x^2+21*x+16", "y^2=29*x^6+13*x^5+23*x^4+24*x^3+25*x^2+25*x+16", "y^2=6*x^6+7*x^5+23*x^4+6*x^3+28*x^2+22*x+6", "y^2=19*x^6+14*x^5+22*x^4+20*x^3+29*x^2+25*x+2", "y^2=3*x^6+25*x^5+22*x^4+8*x^3+18*x^2+11*x+24", "y^2=4*x^6+7*x^5+24*x^4+23*x^3+6*x^2+3*x+23", "y^2=14*x^6+23*x^5+8*x^4+26*x^3+12*x^2+28*x+19", "y^2=7*x^6+13*x^5+9*x^4+9*x^3+29*x^2+29*x+2", "y^2=19*x^6+17*x^5+26*x^4+26*x^3+15*x^2+15*x+8", "y^2=10*x^6+21*x^5+18*x^4+20*x^3+12*x^2+17*x+5", "y^2=20*x^6+27*x^5+6*x^4+5*x^3+13*x^2+17*x+7", "y^2=16*x^6+17*x^5+7*x^4+6*x^3+13*x^2+11*x+14", "y^2=29*x^6+14*x^5+19*x^4+18*x^3+28*x^2+20*x+19", "y^2=24*x^6+25*x^5+x^4+18*x^3+8*x^2+4*x+10", "y^2=23*x^6+9*x^5+5*x^4+24*x^3+28*x^2+20*x+5", "y^2=13*x^6+27*x^5+30*x^4+6*x^3+9*x^2+5*x+8", "y^2=30*x^6+24*x^5+28*x^4+6*x^3+5*x^2+16*x+29", "y^2=5*x^6+20*x^5+25*x^4+12*x^3+24*x^2+27*x+23", "y^2=x^6+6*x^5+22*x^4+9*x^3+11*x+1", "y^2=15*x^6+21*x^5+x^4+27*x^3+18*x^2+30*x+16", "y^2=16*x^6+29*x^5+24*x^4+11*x^3+x^2+2*x+18", "y^2=30*x^6+21*x^5+11*x^4+20*x^2+14*x+28", "y^2=17*x^6+12*x^5+6*x^4+29*x^2+2*x+21", "y^2=2*x^6+16*x^5+9*x^4+24*x^3+16*x^2+18*x+16", "y^2=26*x^6+2*x^5+14*x^4+10*x^3+x^2+10*x+30", "y^2=x^6+17*x^5+27*x^4+18*x^3+2*x^2+5*x+25", "y^2=27*x^6+15*x^5+2*x^4+2*x^3+12*x^2+15*x+16", "y^2=13*x^6+9*x^5+29*x^4+18*x^3+26*x^2+18*x+14", "y^2=17*x^6+19*x^4+22*x^3+7*x^2+8*x+20", "y^2=25*x^6+20*x^5+21*x^4+23*x^3+6*x^2+29*x+21", "y^2=3*x^6+30*x^5+28*x^4+22*x^3+23*x^2+30*x+28", "y^2=20*x^6+9*x^5+8*x^4+20*x^3+23*x^2+19*x+13"], "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": ["4T3"], "geom_dim1_distinct": 0, "geom_dim1_factors": 0, "geom_dim2_distinct": 1, "geom_dim2_factors": 1, "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": ["4T3"], "geometric_number_fields": ["4.0.14912.2"], "geometric_splitting_field": "4.0.14912.2", "geometric_splitting_polynomials": [[17, -10, 11, -2, 1]], "group_structure_count": 5, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 54, "is_cyclic": false, "is_geometrically_simple": true, "is_geometrically_squarefree": true, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 54, "label": "2.31.i_bu", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 2, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [2], "number_fields": ["4.0.14912.2"], "p": 31, "p_rank": 2, "p_rank_deficit": 0, "pic_prime_gens": [[1, 17, 1, 12], [1, 31, 1, 24]], "poly": [1, 8, 46, 248, 961], "poly_str": "1 8 46 248 961 ", "primitive_models": [], "principal_polarization_count": 54, "q": 31, "real_poly": [1, 8, -16], "simple_distinct": ["2.31.i_bu"], "simple_factors": ["2.31.i_buA"], "simple_multiplicities": [1], "singular_primes": ["2,-3*F^2-V-8"], "size": 108, "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.14912.2", "splitting_polynomials": [[17, -10, 11, -2, 1]], "twist_count": 2, "twists": [["2.31.ai_bu", "2.961.bc_cs", 2]], "weak_equivalence_count": 15, "zfv_index": 64, "zfv_index_factorization": [[2, 6]], "zfv_is_bass": false, "zfv_is_maximal": false, "zfv_pic_size": 24, "zfv_plus_index": 4, "zfv_plus_index_factorization": [[2, 2]], "zfv_plus_norm": 3728, "zfv_singular_count": 2, "zfv_singular_primes": ["2,-3*F^2-V-8"]}