# Stored data for abelian variety isogeny class 2.31.e_co, downloaded from the LMFDB on 10 November 2025.
{"abvar_count": 1156, "abvar_counts": [1156, 1040400, 876988996, 850231526400, 820109499102916, 787712305497296400, 756926533207213005316, 727422725458241818214400, 699054162997232529206510596, 671790506959102629859670250000], "abvar_counts_str": "1156 1040400 876988996 850231526400 820109499102916 787712305497296400 756926533207213005316 727422725458241818214400 699054162997232529206510596 671790506959102629859670250000 ", "angle_corank": 1, "angle_rank": 1, "angles": [0.557482058975517, 0.557482058975517], "center_dim": 2, "curve_count": 36, "curve_counts": [36, 1078, 29436, 920638, 28645956, 887559478, 27511981596, 852890572798, 26439642697956, 819628260310198], "curve_counts_str": "36 1078 29436 920638 28645956 887559478 27511981596 852890572798 26439642697956 819628260310198 ", "curves": ["y^2=5*x^6+30*x^5+10*x^4+8*x^3+10*x^2+30*x+5", "y^2=25*x^6+12*x^5+16*x^4+11*x^3+28*x^2+10*x+3", "y^2=3*x^6+15*x^3+3", "y^2=3*x^6+30*x^3+24", "y^2=26*x^6+4*x^5+5*x^4+4*x^3+5*x^2+4*x+26", "y^2=10*x^6+22*x^5+3*x^4+29*x^3+30*x^2+30*x+18", "y^2=10*x^6+3*x^5+5*x^4+16*x^3+5*x^2+3*x+10", "y^2=28*x^6+7*x^5+x^4+25*x^3+5*x^2+13*x+2", "y^2=21*x^6+2*x^5+11*x^4+25*x^3+18*x^2+20", "y^2=6*x^6+22*x^5+11*x^4+11*x^3+27*x^2+28*x+5", "y^2=5*x^6+25*x^5+28*x^3+10*x+18", "y^2=27*x^6+19*x^5+5*x^4+24*x^3+12*x^2+18*x+5", "y^2=21*x^6+21*x^5+28*x^4+15*x^3+22*x^2+25*x+15", "y^2=18*x^6+19*x^5+20*x^4+2*x^3+20*x^2+19*x+18", "y^2=9*x^6+20*x^5+23*x^4+17*x^3+27*x^2+5*x+5", "y^2=30*x^6+x^5+22*x^4+20*x^3+18*x^2+17*x+30", "y^2=6*x^6+4*x^5+29*x^4+2*x^3+17*x^2+10*x+12", "y^2=5*x^6+25*x^5+25*x^4+2*x^3+10*x^2+15*x+13", "y^2=20*x^6+17*x^4+17*x^2+20", "y^2=15*x^6+23*x^5+2*x^4+25*x^3+2*x^2+23*x+15", "y^2=3*x^6+12*x^5+15*x^3+21*x^2+19*x+6", "y^2=15*x^6+26*x^4+26*x^2+15", "y^2=8*x^6+8*x^5+17*x^4+26*x^3+15*x^2+22*x+1", "y^2=6*x^6+6*x^5+27*x^4+14*x^3+27*x^2+6*x+6"], "dim1_distinct": 1, "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, "g": 2, "galois_groups": ["2T1"], "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": 1, "geometric_galois_groups": ["2T1"], "geometric_number_fields": ["2.0.120.1"], "geometric_splitting_field": "2.0.120.1", "geometric_splitting_polynomials": [[30, 0, 1]], "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 24, "is_geometrically_simple": false, "is_geometrically_squarefree": false, "is_primitive": true, "is_simple": false, "is_squarefree": false, "is_supersingular": false, "jacobian_count": 24, "label": "2.31.e_co", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 6, "newton_coelevation": 2, "newton_elevation": 0, "number_fields": ["2.0.120.1"], "p": 31, "p_rank": 2, "p_rank_deficit": 0, "poly": [1, 4, 66, 124, 961], "poly_str": "1 4 66 124 961 ", "primitive_models": [], "q": 31, "real_poly": [1, 4, 4], "simple_distinct": ["1.31.c"], "simple_factors": ["1.31.cA", "1.31.cB"], "simple_multiplicities": [2], "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "2.0.120.1", "splitting_polynomials": [[30, 0, 1]], "twist_count": 6, "twists": [["2.31.ae_co", "2.961.em_hvi", 2], ["2.31.a_cg", "2.961.em_hvi", 2], ["2.31.ac_abb", "2.29791.ans_ffag", 3], ["2.31.a_acg", "2.923521.aegy_ipkhq", 4], ["2.31.c_abb", "2.887503681.deoa_igxkhny", 6]]}