# Stored data for abelian variety isogeny class 2.31.k_ck, downloaded from the LMFDB on 27 March 2026.
{"abvar_count": 1344, "abvar_counts": [1344, 946176, 889648704, 851558400000, 819429371632704, 787764198542340096, 756934818420883255104, 727422926873945702400000, 699053463658703723292281664, 671790583090037069575401762816], "abvar_counts_str": "1344 946176 889648704 851558400000 819429371632704 787764198542340096 756934818420883255104 727422926873945702400000 699053463658703723292281664 671790583090037069575401762816 ", "angle_corank": 1, "angle_rank": 1, "angles": [0.5, 0.854999228987298], "center_dim": 4, "cohen_macaulay_max": 2, "curve_count": 42, "curve_counts": [42, 986, 29862, 922078, 28622202, 887617946, 27512282742, 852890808958, 26439616247562, 819628353194906], "curve_counts_str": "42 986 29862 922078 28622202 887617946 27512282742 852890808958 26439616247562 819628353194906 ", "curves": ["y^2=5*x^6+19*x^5+20*x^4+4*x^3+2*x^2+24*x+4", "y^2=25*x^6+18*x^5+18*x^4+4*x^2+20*x+30", "y^2=5*x^6+9*x^5+30*x^4+29*x^3+28*x^2+19*x+2", "y^2=4*x^6+28*x^5+14*x^3+11*x^2+14*x", "y^2=10*x^6+28*x^5+4*x^4+22*x^3+19*x+28", "y^2=16*x^5+13*x^4+9*x^3+29*x^2+29*x+26", "y^2=26*x^6+10*x^5+17*x^4+16*x^3+11*x^2+16*x+19", "y^2=9*x^6+30*x^5+13*x^4+26*x^3+29*x^2+17*x+7", "y^2=22*x^6+24*x^5+27*x^4+8*x^3+21*x^2+24*x+18", "y^2=18*x^5+24*x^4+7*x^3+27*x^2+16*x", "y^2=16*x^6+8*x^5+6*x^4+11*x^3+6*x^2+8*x+16", "y^2=10*x^6+27*x^5+6*x^4+7*x^3+11*x^2+3*x+11", "y^2=x^6+24*x^5+18*x^4+19*x^3+24*x^2+18*x+20", "y^2=8*x^6+12*x^5+3*x^4+18*x^3+11*x^2+5*x+15", "y^2=26*x^6+28*x^5+15*x^4+24*x^3+14*x^2+19*x+21", "y^2=12*x^6+17*x^5+16*x^4+17*x^3+25*x^2+x+28", "y^2=7*x^6+15*x^5+2*x^4+11*x^3+4*x^2+24*x+24", "y^2=7*x^6+2*x^5+13*x^2+29*x+18", "y^2=20*x^6+5*x^5+3*x^4+21*x^3+9*x^2+22*x+20", "y^2=19*x^6+8*x^5+27*x^4+4*x^3+29*x^2+14*x+17", "y^2=2*x^6+x^4+27*x^3+18*x^2+9*x+23", "y^2=14*x^6+27*x^5+20*x^4+15*x^3+10*x^2+30*x+25", "y^2=26*x^6+5*x^5+28*x^4+24*x^3+28*x^2+5*x+26", "y^2=15*x^6+8*x^5+14*x^4+30*x^3+x^2+x+28", "y^2=30*x^6+5*x^5+25*x^4+5*x^3+3*x^2+11*x+16", "y^2=9*x^6+14*x^5+26*x^4+9*x^3+17*x^2+18*x+20", "y^2=14*x^6+20*x^5+9*x^4+26*x^3+9*x^2+20*x+14", "y^2=7*x^6+9*x^4+x^3+23*x^2+13*x+10", "y^2=14*x^6+14*x^5+28*x^4+7*x^3+23*x^2+25*x+2", "y^2=13*x^6+24*x^5+2*x^4+7*x^3+20*x^2+16*x+2", "y^2=4*x^6+30*x^5+30*x^4+3*x^3+30*x^2+6*x+22", "y^2=16*x^6+6*x^5+24*x^4+11*x^3+15*x^2+19*x+30", "y^2=x^6+17*x^5+25*x^4+16*x^3+26*x^2+19*x+22", "y^2=x^6+4*x^5+21*x^4+11*x^3+22*x^2+17*x+4", "y^2=8*x^6+8*x^5+28*x^4+12*x^3+6*x^2+2*x+29", "y^2=11*x^6+7*x^5+17*x^4+15*x^3+25*x^2+24*x+1", "y^2=19*x^6+23*x^5+20*x^4+16*x^3+25*x^2+3*x+25", "y^2=28*x^6+9*x^5+27*x^4+22*x^3+27*x^2+9*x+28", "y^2=8*x^6+17*x^5+29*x^4+7*x^3+27*x^2+9*x", "y^2=5*x^6+17*x^5+8*x^4+11*x^3+10*x^2+22*x+20", "y^2=26*x^6+18*x^4+6*x^3+14*x^2+14*x+25", "y^2=8*x^6+x^5+11*x^4+24*x^3+22*x^2+13*x+28", "y^2=19*x^6+3*x^5+19*x^4+12*x^3+x^2+11*x+14", "y^2=2*x^6+15*x^5+14*x^4+7*x^3+14*x^2+15*x+2", "y^2=4*x^6+5*x^5+26*x^4+23*x^3+2*x^2+20*x+9", "y^2=5*x^6+19*x^5+9*x^4+24*x^3+11*x^2+6*x+14", "y^2=17*x^5+21*x^4+12*x^2+6*x+22", "y^2=x^6+28*x^5+2*x^4+28*x^3+2*x^2+19*x+9", "y^2=21*x^6+17*x^5+9*x^4+17*x^3+7*x^2+8*x+21", "y^2=28*x^6+5*x^5+13*x^4+22*x^3+17*x^2+27*x+26", "y^2=17*x^6+x^5+5*x^4+28*x^3+x^2+12*x+25", "y^2=17*x^6+3*x^4+8*x^3+22*x^2+6", "y^2=x^6+17*x^5+17*x^4+15*x^3+17*x^2+17*x+1", "y^2=9*x^6+29*x^5+4*x^4+2*x^3+x^2+9*x+10", "y^2=6*x^6+12*x^5+6*x^4+29*x^3+7*x^2+27", "y^2=17*x^6+2*x^5+22*x^4+25*x^3+27*x+29", "y^2=x^6+6*x^5+14*x^4+x^3+13*x^2+26*x+19", "y^2=x^6+17*x^5+27*x^3+19*x^2+13*x+5", "y^2=4*x^6+7*x^5+12*x^4+12*x^3+10*x^2+9*x+20", "y^2=21*x^6+12*x^5+12*x^4+22*x^3+19*x^2+17*x+23"], "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": 24, "g": 2, "galois_groups": ["2T1", "2T1"], "geom_dim1_distinct": 2, "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": 3, "geometric_extension_degree": 2, "geometric_galois_groups": ["1T1", "2T1"], "geometric_number_fields": ["1.1.1.1", "2.0.24.1"], "geometric_splitting_field": "2.0.24.1", "geometric_splitting_polynomials": [[6, 0, 1]], "group_structure_count": 4, "has_geom_ss_factor": true, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 60, "is_cyclic": false, "is_geometrically_simple": false, "is_geometrically_squarefree": true, "is_primitive": true, "is_simple": false, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 60, "label": "2.31.k_ck", "max_divalg_dim": 1, "max_geom_divalg_dim": 4, "max_twist_degree": 2, "newton_coelevation": 1, "newton_elevation": 1, "noncyclic_primes": [2], "number_fields": ["2.0.31.1", "2.0.24.1"], "p": 31, "p_rank": 1, "p_rank_deficit": 1, "poly": [1, 10, 62, 310, 961], "poly_str": "1 10 62 310 961 ", "primitive_models": [], "q": 31, "real_poly": [1, 10], "simple_distinct": ["1.31.a", "1.31.k"], "simple_factors": ["1.31.aA", "1.31.kA"], "simple_multiplicities": [1, 1], "singular_primes": ["2,3*F-11", "5,-3*F-21", "5,22*F-14"], "slopes": ["0A", "1/2A", "1/2B", "1A"], "splitting_field": "4.0.553536.1", "splitting_polynomials": [[10, -28, 29, -2, 1]], "twist_count": 2, "twists": [["2.31.ak_ck", "2.961.y_aqs", 2]], "weak_equivalence_count": 28, "zfv_index": 200, "zfv_index_factorization": [[2, 3], [5, 2]], "zfv_is_bass": false, "zfv_is_maximal": false, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 2976, "zfv_singular_count": 6, "zfv_singular_primes": ["2,3*F-11", "5,-3*F-21", "5,22*F-14"]}