# Stored data for abelian variety isogeny class 2.31.a_bl, downloaded from the LMFDB on 28 July 2026.
{"abvar_count": 999, "abvar_counts": [999, 998001, 887447664, 853914605625, 819628283788479, 787563356339056896, 756943935274295474319, 727425750758891064755625, 699053619999018401684339184, 671790523586047467524813133441], "abvar_counts_str": "999 998001 887447664 853914605625 819628283788479 787563356339056896 756943935274295474319 727425750758891064755625 699053619999018401684339184 671790523586047467524813133441 ", "angle_corank": 1, "angle_rank": 1, "angles": [0.351775594289712, 0.648224405710288], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 32, "curve_counts": [32, 1036, 29792, 924628, 28629152, 887391646, 27512614112, 852894119908, 26439622160672, 819628280596156], "curve_counts_str": "32 1036 29792 924628 28629152 887391646 27512614112 852894119908 26439622160672 819628280596156 ", "curves": ["y^2=23*x^6+23*x^5+29*x^4+23*x^3+x^2+29*x+1", "y^2=14*x^6+21*x^5+23*x^4+20*x^3+3*x^2+7*x+9", "y^2=11*x^6+x^5+7*x^4+29*x^3+9*x^2+21*x+27", "y^2=20*x^6+10*x^5+30*x^4+17*x^3+16*x^2+19*x+4", "y^2=29*x^6+30*x^5+28*x^4+20*x^3+17*x^2+26*x+12", "y^2=19*x^6+9*x^5+17*x^4+20*x^3+10*x^2+15*x+7", "y^2=26*x^6+27*x^5+20*x^4+29*x^3+30*x^2+14*x+21", "y^2=26*x^6+2*x^5+9*x^4+25*x^3+16*x^2+12*x+18", "y^2=16*x^6+6*x^5+27*x^4+13*x^3+17*x^2+5*x+23", "y^2=13*x^6+x^5+23*x^4+3*x^3+21*x^2+19*x+22", "y^2=8*x^6+3*x^5+7*x^4+9*x^3+x^2+26*x+4", "y^2=17*x^6+2*x^5+15*x^4+23*x^3+26*x^2+21", "y^2=20*x^6+6*x^5+14*x^4+7*x^3+16*x^2+1", "y^2=4*x^6+18*x^5+20*x^4+10*x^3+7*x^2+x+24", "y^2=12*x^6+23*x^5+29*x^4+30*x^3+21*x^2+3*x+10", "y^2=10*x^6+6*x^5+19*x^4+16*x^3+25*x^2+4*x+24", "y^2=30*x^6+18*x^5+26*x^4+17*x^3+13*x^2+12*x+10", "y^2=28*x^6+11*x^5+9*x^4+x^3+21*x^2+22*x+17", "y^2=15*x^6+10*x^5+26*x^4+2*x^3+8*x^2+2*x+2", "y^2=14*x^6+30*x^5+16*x^4+6*x^3+24*x^2+6*x+6", "y^2=26*x^6+5*x^4+23*x^3+27*x^2+26*x+24", "y^2=16*x^6+15*x^4+7*x^3+19*x^2+16*x+10", "y^2=21*x^6+24*x^5+15*x^4+29*x^3+29*x^2+12*x+11", "y^2=x^6+10*x^5+14*x^4+25*x^3+25*x^2+5*x+2", "y^2=3*x^6+15*x^5+8*x^4+13*x^3+25*x^2+6*x+2", "y^2=9*x^6+14*x^5+24*x^4+8*x^3+13*x^2+18*x+6", "y^2=11*x^6+26*x^5+24*x^4+11*x^3+23*x^2+27*x+26", "y^2=2*x^6+16*x^5+10*x^4+2*x^3+7*x^2+19*x+16", "y^2=29*x^6+29*x^5+7*x^4+6*x^3+4*x^2+11*x+3", "y^2=25*x^6+25*x^5+21*x^4+18*x^3+12*x^2+2*x+9", "y^2=12*x^6+30*x^5+8*x^4+20*x^3+14*x^2+x+26", "y^2=5*x^6+28*x^5+24*x^4+29*x^3+11*x^2+3*x+16", "y^2=24*x^6+6*x^5+14*x^4+19*x^3+10*x^2+2*x+19", "y^2=10*x^6+18*x^5+11*x^4+26*x^3+30*x^2+6*x+26", "y^2=20*x^6+26*x^5+6*x^4+28*x^2+8*x+28", "y^2=29*x^6+16*x^5+18*x^4+22*x^2+24*x+22", "y^2=30*x^6+30*x^5+21*x^4+7*x^3+24*x^2+7*x+10", "y^2=28*x^6+28*x^5+x^4+21*x^3+10*x^2+21*x+30", "y^2=13*x^6+12*x^5+6*x^4+13*x^3+9*x^2+20*x+11", "y^2=8*x^6+5*x^5+18*x^4+8*x^3+27*x^2+29*x+2", "y^2=29*x^6+22*x^5+3*x^4+3*x^3+30*x^2+25*x+2", "y^2=25*x^6+4*x^5+9*x^4+9*x^3+28*x^2+13*x+6", "y^2=25*x^6+3*x^5+5*x^4+15*x^3+5*x^2+3*x+25", "y^2=13*x^6+9*x^5+15*x^4+14*x^3+15*x^2+9*x+13", "y^2=7*x^6+8*x^4+20*x^3+23*x^2+24", "y^2=2*x^6+26*x^5+6*x^4+10*x^3+8*x^2+23*x+29", "y^2=6*x^6+16*x^5+18*x^4+30*x^3+24*x^2+7*x+25", "y^2=27*x^6+15*x^5+25*x^4+4*x^3+14*x^2+30*x+29", "y^2=19*x^6+14*x^5+13*x^4+12*x^3+11*x^2+28*x+25", "y^2=10*x^6+3*x^5+14*x^4+16*x^3+4*x^2+20*x+16", "y^2=30*x^6+9*x^5+11*x^4+17*x^3+12*x^2+29*x+17", "y^2=15*x^6+28*x^5+8*x^4+4*x^3+29*x^2+7*x+15", "y^2=14*x^6+22*x^5+24*x^4+12*x^3+25*x^2+21*x+14", "y^2=26*x^6+9*x^5+30*x^4+16*x^3+15*x^2+10*x+11", "y^2=16*x^6+27*x^5+28*x^4+17*x^3+14*x^2+30*x+2", "y^2=24*x^6+4*x^5+23*x^4+15*x^3+23*x^2+10*x+11", "y^2=10*x^6+12*x^5+7*x^4+14*x^3+7*x^2+30*x+2", "y^2=11*x^6+17*x^5+26*x^4+18*x^3+2*x^2+30*x+5", "y^2=27*x^6+x^4+20*x^3+11*x^2+8", "y^2=28*x^6+6*x^5+3*x^3+8*x^2+24*x+4", "y^2=22*x^6+18*x^5+9*x^3+24*x^2+10*x+12", "y^2=10*x^6+2*x^5+x^4+8*x^3+12*x^2+9*x+12", "y^2=30*x^6+6*x^5+3*x^4+24*x^3+5*x^2+27*x+5", "y^2=30*x^6+28*x^5+14*x^4+18*x^3+25*x^2+17*x+19", "y^2=28*x^6+22*x^5+11*x^4+23*x^3+13*x^2+20*x+26", "y^2=19*x^6+30*x^5+x^4+4*x^3+9*x^2+25*x+11", "y^2=26*x^6+28*x^5+3*x^4+12*x^3+27*x^2+13*x+2", "y^2=4*x^6+5*x^5+15*x^4+28*x^3+6*x^2+19*x+6", "y^2=12*x^6+15*x^5+14*x^4+22*x^3+18*x^2+26*x+18", "y^2=11*x^6+26*x^5+21*x^4+19*x^3+30*x^2+15*x+26", "y^2=2*x^6+16*x^5+x^4+26*x^3+28*x^2+14*x+16", "y^2=2*x^6+9*x^5+8*x^4+16*x^3+15*x^2+5*x+15", "y^2=13*x^6+20*x^5+30*x^4+14*x^3+20*x^2+20*x+5", "y^2=8*x^6+29*x^5+28*x^4+11*x^3+29*x^2+29*x+15", "y^2=25*x^6+20*x^5+16*x^4+6*x^3+2*x^2+10*x+19", "y^2=13*x^6+29*x^5+17*x^4+18*x^3+6*x^2+30*x+26", "y^2=25*x^6+24*x^5+x^4+21*x^3+7*x^2+29*x+19", "y^2=13*x^6+10*x^5+3*x^4+x^3+21*x^2+25*x+26", "y^2=9*x^6+26*x^5+20*x^4+29*x^3+5*x^2+21*x+20", "y^2=27*x^6+16*x^5+29*x^4+25*x^3+15*x^2+x+29", "y^2=17*x^6+11*x^5+25*x^4+9*x^3+30*x^2+13*x+22", "y^2=20*x^6+2*x^5+13*x^4+27*x^3+28*x^2+8*x+4", "y^2=3*x^6+7*x^5+15*x^4+3*x^3+26*x^2+18*x+24", "y^2=9*x^6+21*x^5+14*x^4+9*x^3+16*x^2+23*x+10", "y^2=4*x^6+23*x^5+25*x^4+16*x^3+30*x^2+12*x+6", "y^2=12*x^6+7*x^5+13*x^4+17*x^3+28*x^2+5*x+18", "y^2=6*x^6+29*x^5+25*x^4+24*x^3+26*x^2+28*x+27", "y^2=18*x^6+25*x^5+13*x^4+10*x^3+16*x^2+22*x+19", "y^2=18*x^6+x^5+26*x^4+20*x^3+5*x^2+27*x+28", "y^2=23*x^6+3*x^5+16*x^4+29*x^3+15*x^2+19*x+22"], "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": 32, "g": 2, "galois_groups": ["2T1", "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": 2, "geometric_galois_groups": ["2T1"], "geometric_number_fields": ["2.0.11.1"], "geometric_splitting_field": "2.0.11.1", "geometric_splitting_polynomials": [[3, -1, 1]], "group_structure_count": 2, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 90, "is_cyclic": false, "is_geometrically_simple": false, "is_geometrically_squarefree": false, "is_primitive": true, "is_simple": false, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 90, "label": "2.31.a_bl", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 6, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [3], "number_fields": ["2.0.11.1", "2.0.11.1"], "p": 31, "p_rank": 2, "p_rank_deficit": 0, "poly": [1, 0, 37, 0, 961], "poly_str": "1 0 37 0 961 ", "primitive_models": [], "q": 31, "real_poly": [1, 0, -25], "simple_distinct": ["1.31.af", "1.31.f"], "simple_factors": ["1.31.afA", "1.31.fA"], "simple_multiplicities": [1, 1], "singular_primes": ["3,-2*F-22", "2,-F^2-V-44", "5,F+37", "5,-7*F-11", "3,-4*F-7"], "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "2.0.11.1", "splitting_polynomials": [[3, -1, 1]], "twist_count": 6, "twists": [["2.31.ak_dj", "2.961.cw_ewp", 2], ["2.31.k_dj", "2.961.cw_ewp", 2], ["2.31.a_abl", "2.923521.bqo_esmrz", 4], ["2.31.af_ag", "2.887503681.agjtc_pxnegnm", 6], ["2.31.f_ag", "2.887503681.agjtc_pxnegnm", 6]], "weak_equivalence_count": 32, "zfv_index": 900, "zfv_index_factorization": [[2, 2], [3, 2], [5, 2]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 9801, "zfv_singular_count": 10, "zfv_singular_primes": ["3,-2*F-22", "2,-F^2-V-44", "5,F+37", "5,-7*F-11", "3,-4*F-7"]}