# Stored data for abelian variety isogeny class 2.31.a_be, downloaded from the LMFDB on 13 February 2026.
{"abvar_count": 992, "abvar_counts": [992, 984064, 887444192, 854781607936, 819628320073952, 787557193914532864, 756943935241915385312, 727424490738585600000000, 699053619998992892635769312, 671790583067248707046748898304], "abvar_counts_str": "992 984064 887444192 854781607936 819628320073952 787557193914532864 756943935241915385312 727424490738585600000000 699053619998992892635769312 671790583067248707046748898304 ", "angle_corank": 1, "angle_rank": 1, "angles": [0.33038479927828, 0.66961520072172], "center_dim": 4, "cohen_macaulay_max": 3, "curve_count": 32, "curve_counts": [32, 1022, 29792, 925566, 28629152, 887384702, 27512614112, 852892642558, 26439622160672, 819628353167102], "curve_counts_str": "32 1022 29792 925566 28629152 887384702 27512614112 852892642558 26439622160672 819628353167102 ", "curves": ["y^2=28*x^6+26*x^5+26*x^4+24*x^3+22*x^2+6*x+2", "y^2=13*x^5+17*x^4+20*x^3+16*x^2+9*x", "y^2=8*x^5+20*x^4+29*x^3+17*x^2+27*x", "y^2=22*x^6+26*x^5+13*x^4+26*x^3+16*x^2+30*x+20", "y^2=14*x^6+6*x^5+21*x^4+19*x^3+21*x^2+12*x+30", "y^2=11*x^6+18*x^5+x^4+26*x^3+x^2+5*x+28", "y^2=9*x^6+x^5+2*x^4+16*x^3+24*x^2+20*x+21", "y^2=8*x^6+5*x^5+24*x^3+21*x^2+18*x+24", "y^2=8*x^6+14*x^5+21*x^4+4*x^3+5*x+4", "y^2=24*x^6+11*x^5+x^4+12*x^3+15*x+12", "y^2=x^6+24*x^5+30*x^4+16*x^3+7*x^2+29*x+29", "y^2=10*x^5+3*x^4+9*x^3+4*x^2+30*x+1", "y^2=30*x^5+9*x^4+27*x^3+12*x^2+28*x+3", "y^2=2*x^6+20*x^5+25*x^4+13*x^2+6*x+23", "y^2=20*x^6+17*x^5+14*x^4+27*x^3+14*x^2+22*x+15", "y^2=29*x^6+20*x^5+11*x^4+19*x^3+11*x^2+4*x+14", "y^2=20*x^6+22*x^5+18*x^4+4*x^3+27*x^2+3*x+21", "y^2=11*x^6+24*x^5+12*x^4+22*x^3+18*x^2+21*x", "y^2=2*x^6+10*x^5+5*x^4+4*x^3+23*x^2+x", "y^2=4*x^6+14*x^5+19*x^4+22*x^3+30*x^2+27*x+15", "y^2=12*x^6+11*x^5+26*x^4+4*x^3+28*x^2+19*x+14", "y^2=22*x^6+10*x^5+17*x^4+12*x^3+27*x^2+24*x+18", "y^2=23*x^6+5*x^5+16*x^4+6*x^3+4*x^2+7*x+8", "y^2=7*x^6+15*x^5+17*x^4+18*x^3+12*x^2+21*x+24", "y^2=11*x^6+11*x^5+15*x^4+25*x^3+4*x^2+19*x+25", "y^2=2*x^6+2*x^5+14*x^4+13*x^3+12*x^2+26*x+13", "y^2=12*x^6+16*x^5+x^4+8*x^3+10*x^2+7*x+6", "y^2=5*x^6+17*x^5+3*x^4+24*x^3+30*x^2+21*x+18", "y^2=20*x^6+14*x^5+10*x^4+25*x^3+23*x^2+9*x+9", "y^2=29*x^6+11*x^5+30*x^4+13*x^3+7*x^2+27*x+27", "y^2=7*x^6+8*x^5+20*x^4+3*x^3+23*x^2+9*x+18", "y^2=23*x^6+30*x^5+6*x^4+10*x^3+2*x^2+24*x+2", "y^2=7*x^6+5*x^5+17*x^4+22*x^2+25*x+2", "y^2=21*x^6+15*x^5+20*x^4+4*x^2+13*x+6", "y^2=17*x^6+26*x^5+13*x^4+14*x^3+17*x^2+28*x+4", "y^2=21*x^6+10*x^5+19*x^4+26*x^2+3*x+9", "y^2=5*x^6+27*x^5+17*x^3+12*x+21", "y^2=22*x^5+x^4+24*x^3+27*x+28", "y^2=4*x^5+3*x^4+10*x^3+19*x+22", "y^2=17*x^6+21*x^5+30*x^4+11*x^3+24*x^2+19*x+8", "y^2=20*x^6+x^5+28*x^4+2*x^3+10*x^2+26*x+24", "y^2=25*x^6+13*x^5+3*x^4+26*x^3+23*x^2+22*x+28", "y^2=30*x^6+11*x^5+13*x^4+5*x^3+13*x^2+12*x+27", "y^2=28*x^6+2*x^5+8*x^4+15*x^3+8*x^2+5*x+19", "y^2=29*x^6+25*x^5+22*x^4+24*x^3+4*x^2+17*x+8", "y^2=27*x^6+25*x^5+23*x^4+5*x^2+10*x+29", "y^2=5*x^6+14*x^5+22*x^3+14*x^2+3*x+12", "y^2=15*x^6+11*x^5+4*x^3+11*x^2+9*x+5", "y^2=16*x^6+7*x^5+30*x^4+7*x^3+24*x^2+22*x+9", "y^2=17*x^6+21*x^5+28*x^4+21*x^3+10*x^2+4*x+27", "y^2=13*x^6+2*x^5+12*x^4+7*x^3+21*x^2+20*x+4", "y^2=27*x^6+28*x^5+17*x^4+18*x^3+8*x^2+13*x+16", "y^2=19*x^6+22*x^5+20*x^4+23*x^3+24*x^2+8*x+17", "y^2=27*x^6+23*x^5+8*x^4+29*x^3+17*x^2+21*x+16", "y^2=19*x^6+7*x^5+24*x^4+25*x^3+20*x^2+x+17", "y^2=10*x^6+4*x^5+14*x^4+x^3+11*x^2+6*x+19", "y^2=30*x^6+12*x^5+11*x^4+3*x^3+2*x^2+18*x+26", "y^2=24*x^6+12*x^5+25*x^4+14*x+26", "y^2=10*x^6+5*x^5+13*x^4+11*x+16", "y^2=8*x^6+15*x^5+30*x^4+30*x^3+19*x^2+19*x+23", "y^2=24*x^6+14*x^5+28*x^4+28*x^3+26*x^2+26*x+7", "y^2=20*x^6+18*x^5+30*x^4+9*x^3+21*x^2+6*x+24", "y^2=6*x^6+14*x^5+2*x^4+11*x^3+13*x^2+20*x", "y^2=18*x^6+11*x^5+6*x^4+2*x^3+8*x^2+29*x", "y^2=x^6+9*x^5+29*x^4+9*x^3+27*x^2+10*x+18", "y^2=2*x^6+29*x^5+19*x^4+25*x^3+22*x^2+20*x+29", "y^2=6*x^6+25*x^5+26*x^4+13*x^3+4*x^2+29*x+25", "y^2=17*x^6+20*x^5+9*x^4+12*x^3+28*x^2+10*x+26", "y^2=20*x^6+29*x^5+27*x^4+5*x^3+22*x^2+30*x+16", "y^2=22*x^6+18*x^5+26*x^4+29*x^3+3*x^2+26", "y^2=4*x^6+23*x^5+16*x^4+25*x^3+9*x^2+16", "y^2=19*x^6+14*x^5+25*x^4+4*x^3+22*x^2+24*x", "y^2=24*x^6+21*x^5+30*x^4+16*x^3+22*x^2+13*x+19", "y^2=10*x^6+x^5+28*x^4+17*x^3+4*x^2+8*x+26", "y^2=22*x^6+22*x^5+22*x^4+x^3+28*x^2+21*x+10", "y^2=4*x^6+4*x^5+4*x^4+3*x^3+22*x^2+x+30", "y^2=10*x^6+25*x^5+24*x^4+10*x^3+18*x^2+16*x+11", "y^2=26*x^6+6*x^5+29*x^4+19*x^3+9*x^2+13*x+10", "y^2=11*x^6+20*x^5+13*x^4+16*x^3+26*x^2+7", "y^2=2*x^6+29*x^5+8*x^4+17*x^3+16*x^2+21", "y^2=24*x^6+17*x^5+20*x^4+16*x^3+20*x^2+28*x+1", "y^2=10*x^6+20*x^5+29*x^4+17*x^3+29*x^2+22*x+3", "y^2=19*x^6+8*x^5+24*x^4+15*x^3+4*x^2+23*x+14", "y^2=26*x^6+24*x^5+10*x^4+14*x^3+12*x^2+7*x+11", "y^2=24*x^6+19*x^5+27*x^4+7*x^3+3*x^2+28*x+2", "y^2=10*x^6+26*x^5+19*x^4+21*x^3+9*x^2+22*x+6", "y^2=12*x^6+x^5+19*x^3+21*x^2+28*x+23", "y^2=5*x^6+3*x^5+26*x^3+x^2+22*x+7", "y^2=14*x^6+29*x^5+4*x^4+24*x^3+23*x^2+30*x+13", "y^2=11*x^6+25*x^5+12*x^4+10*x^3+7*x^2+28*x+8", "y^2=10*x^6+x^5+11*x^4+6*x^3+19*x^2+14*x+22", "y^2=16*x^6+18*x^5+6*x^4+7*x^3+23*x^2+2*x+13", "y^2=17*x^6+23*x^5+18*x^4+21*x^3+7*x^2+6*x+8", "y^2=15*x^6+5*x^5+23*x^4+11*x^3+17*x^2+6*x+9", "y^2=27*x^6+15*x^5+29*x^4+30*x^3+22*x^2+15*x+18", "y^2=19*x^6+14*x^5+25*x^4+28*x^3+4*x^2+14*x+23", "y^2=29*x^6+8*x^5+30*x^3+18*x^2+15*x+28", "y^2=25*x^6+24*x^5+28*x^3+23*x^2+14*x+22", "y^2=29*x^6+24*x^5+28*x^4+30*x^3+20*x^2+18*x+25", "y^2=25*x^6+10*x^5+22*x^4+28*x^3+29*x^2+23*x+13", "y^2=16*x^6+28*x^5+16*x^4+x^3+8*x^2+21*x", "y^2=24*x^6+23*x^5+20*x^4+27*x^3+29*x^2+8*x+11", "y^2=10*x^6+7*x^5+29*x^4+19*x^3+25*x^2+24*x+2", "y^2=25*x^6+25*x^5+28*x^4+27*x^3+14*x^2+24*x+23", "y^2=13*x^6+13*x^5+22*x^4+19*x^3+11*x^2+10*x+7", "y^2=20*x^6+17*x^5+9*x^4+13*x^3+x^2+9*x+23", "y^2=29*x^6+20*x^5+27*x^4+8*x^3+3*x^2+27*x+7", "y^2=28*x^6+9*x^5+20*x^4+8*x^3+25*x^2+19*x+1", "y^2=22*x^6+27*x^5+29*x^4+24*x^3+13*x^2+26*x+3", "y^2=17*x^6+10*x^5+21*x^4+25*x^3+25*x^2+28*x+8", "y^2=20*x^6+30*x^5+x^4+13*x^3+13*x^2+22*x+24", "y^2=19*x^6+5*x^5+24*x^4+22*x^3+3*x^2+7*x+5", "y^2=26*x^6+15*x^5+10*x^4+4*x^3+9*x^2+21*x+15", "y^2=19*x^6+11*x^5+30*x^4+9*x^3+30*x^2+17*x+3", "y^2=26*x^6+2*x^5+28*x^4+27*x^3+28*x^2+20*x+9", "y^2=24*x^6+23*x^5+13*x^4+18*x^3+24*x^2+3*x+20", "y^2=10*x^6+7*x^5+8*x^4+23*x^3+10*x^2+9*x+29", "y^2=29*x^6+27*x^5+18*x^3+15*x^2+10*x+26", "y^2=25*x^6+19*x^5+23*x^3+14*x^2+30*x+16", "y^2=22*x^6+x^5+20*x^4+11*x^3+26*x^2+13", "y^2=4*x^6+3*x^5+29*x^4+2*x^3+16*x^2+8", "y^2=14*x^6+30*x^5+22*x^4+13*x^3+30*x^2+29*x+15", "y^2=11*x^6+28*x^5+4*x^4+8*x^3+28*x^2+25*x+14", "y^2=20*x^6+26*x^5+29*x^4+8*x^3+25*x^2+x+27", "y^2=29*x^6+16*x^5+25*x^4+24*x^3+13*x^2+3*x+19", "y^2=6*x^6+26*x^5+21*x^4+17*x^3+3*x+14", "y^2=9*x^6+25*x^4+14*x^3+18*x^2+9*x+11", "y^2=27*x^6+13*x^4+11*x^3+23*x^2+27*x+2", "y^2=6*x^6+11*x^5+16*x^4+24*x^3+17*x^2+25*x+14", "y^2=18*x^6+2*x^5+17*x^4+10*x^3+20*x^2+13*x+11"], "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": 14, "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": ["2.0.184.1"], "geometric_splitting_field": "2.0.184.1", "geometric_splitting_polynomials": [[46, 0, 1]], "group_structure_count": 6, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 130, "is_cyclic": false, "is_geometrically_simple": false, "is_geometrically_squarefree": false, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 130, "label": "2.31.a_be", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 8, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [2], "number_fields": ["4.0.33856.2"], "p": 31, "p_rank": 2, "p_rank_deficit": 0, "poly": [1, 0, 30, 0, 961], "poly_str": "1 0 30 0 961 ", "primitive_models": [], "q": 31, "real_poly": [1, 0, -32], "simple_distinct": ["2.31.a_be"], "simple_factors": ["2.31.a_beA"], "simple_multiplicities": [1], "singular_primes": ["2,41*F+44*V-1"], "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.33856.2", "splitting_polynomials": [[62, -8, 9, -2, 1]], "twist_count": 4, "twists": [["2.31.a_abe", "2.923521.daq_ginko", 4], ["2.31.ai_bg", "2.852891037441.dnilg_lgowonody", 8], ["2.31.i_bg", "2.852891037441.dnilg_lgowonody", 8]], "weak_equivalence_count": 23, "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": 8464, "zfv_singular_count": 2, "zfv_singular_primes": ["2,41*F+44*V-1"]}