# Stored data for abelian variety isogeny class 2.31.ak_dj, downloaded from the LMFDB on 14 September 2026.
{"abvar_count": 729, "abvar_counts": [729, 998001, 907937424, 853914605625, 819183221376129, 787563356339056896, 756941785716807052209, 727425750758891064755625, 699054091532917311284933904, 671790523586047467524813133441], "abvar_counts_str": "729 998001 907937424 853914605625 819183221376129 787563356339056896 756941785716807052209 727425750758891064755625 699054091532917311284933904 671790523586047467524813133441 ", "angle_corank": 1, "angle_rank": 1, "angles": [0.351775594289712, 0.351775594289712], "center_dim": 2, "curve_count": 22, "curve_counts": [22, 1036, 30472, 924628, 28613602, 887391646, 27512535982, 852894119908, 26439639995032, 819628280596156], "curve_counts_str": "22 1036 30472 924628 28613602 887391646 27512535982 852894119908 26439639995032 819628280596156 ", "curves": ["y^2=x^6+7*x^3+2", "y^2=20*x^6+19*x^5+12*x^4+21*x^3+12*x^2+19*x+20", "y^2=25*x^6+6*x^5+23*x^4+8*x^3+25*x^2+2*x+20", "y^2=27*x^6+2*x^5+19*x^4+10*x^3+19*x^2+2*x+27", "y^2=17*x^6+5*x^5+19*x^4+26*x^3+19*x^2+5*x+17", "y^2=x^6+25*x^3+1", "y^2=x^6+x^3+1", "y^2=21*x^6+29*x^5+13*x^4+21*x^3+13*x^2+29*x+21", "y^2=x^6+11*x^5+24*x^4+20*x^3+9*x^2+3", "y^2=x^6+24*x^5+13*x^4+7*x^3+13*x^2+24*x+1", "y^2=17*x^6+14*x^5+14*x^4+2*x^3+4*x^2+10*x+23", "y^2=23*x^6+13*x^5+2*x^4+15*x^3+2*x^2+13*x+23", "y^2=16*x^6+21*x^5+12*x^4+7*x^3+12*x^2+21*x+16", "y^2=4*x^6+8*x^5+15*x^4+4*x^3+15*x^2+8*x+4", "y^2=3*x^6+28*x^5+18*x^4+19*x^3+8*x^2+26*x+12", "y^2=28*x^6+15*x^5+6*x^4+19*x^3+6*x^2+15*x+28"], "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": ["2.0.11.1"], "geometric_splitting_field": "2.0.11.1", "geometric_splitting_polynomials": [[3, -1, 1]], "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 16, "is_cyclic": false, "is_geometrically_simple": false, "is_geometrically_squarefree": false, "is_primitive": true, "is_simple": false, "is_squarefree": false, "is_supersingular": false, "jacobian_count": 16, "label": "2.31.ak_dj", "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"], "p": 31, "p_rank": 2, "p_rank_deficit": 0, "poly": [1, -10, 87, -310, 961], "poly_str": "1 -10 87 -310 961 ", "primitive_models": [], "q": 31, "real_poly": [1, -10, 25], "simple_distinct": ["1.31.af"], "simple_factors": ["1.31.afA", "1.31.afB"], "simple_multiplicities": [2], "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "2.0.11.1", "splitting_polynomials": [[3, -1, 1]], "twist_count": 6, "twists": [["2.31.a_bl", "2.961.cw_ewp", 2], ["2.31.k_dj", "2.961.cw_ewp", 2], ["2.31.f_ag", "2.29791.bae_jzdu", 3], ["2.31.a_abl", "2.923521.bqo_esmrz", 4], ["2.31.af_ag", "2.887503681.agjtc_pxnegnm", 6]]}