# Stored data for abelian variety isogeny class 2.31.aj_da, downloaded from the LMFDB on 12 May 2026.
{"abvar_count": 752, "abvar_counts": [752, 998656, 903720512, 853207745536, 819357540167312, 787633230996557824, 756944343980702992208, 727422919141852720041984, 699053527524348661423725632, 671790547832716519747246648576], "abvar_counts_str": "752 998656 903720512 853207745536 819357540167312 787633230996557824 756944343980702992208 727422919141852720041984 699053527524348661423725632 671790547832716519747246648576 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 0, "angle_rank": 2, "angles": [0.299425345193821, 0.429727371569294], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 23, "curve_counts": [23, 1037, 30332, 923865, 28619693, 887470382, 27512628971, 852890799889, 26439618663092, 819628310178677], "curve_counts_str": "23 1037 30332 923865 28619693 887470382 27512628971 852890799889 26439618663092 819628310178677 ", "curves": ["y^2=16*x^6+26*x^5+12*x^4+25*x^3+11*x^2+27", "y^2=15*x^5+21*x^4+25*x^3+12*x^2+11*x", "y^2=11*x^6+22*x^5+2*x^4+20*x^3+4*x^2+22*x+29", "y^2=22*x^6+2*x^5+23*x^4+26*x^3+5*x^2+15*x+27", "y^2=23*x^6+21*x^5+24*x^4+25*x^3+21*x^2+13*x+1", "y^2=18*x^6+10*x^5+29*x^4+12*x^3+22*x^2+14*x+22", "y^2=16*x^6+21*x^5+30*x^4+6*x^3+13*x^2+29*x+27", "y^2=27*x^6+15*x^5+15*x^4+6*x^3+23*x^2+9*x+20", "y^2=12*x^6+13*x^5+13*x^4+29*x^3+15*x^2+25*x+18", "y^2=6*x^6+x^5+16*x^4+3*x^3+26*x^2+14*x+8", "y^2=23*x^6+30*x^5+12*x^4+14*x^3+20*x^2+17*x+11", "y^2=12*x^6+20*x^5+2*x^4+30*x^3+x^2+26*x+21", "y^2=16*x^6+28*x^5+30*x^4+16*x^3+20*x^2+13*x+30", "y^2=13*x^6+9*x^5+23*x^4+24*x^3+5*x^2+27*x+19", "y^2=22*x^6+23*x^4+10*x^3+2*x^2+23", "y^2=10*x^6+18*x^5+x^4+28*x^3+5*x^2+10*x+21", "y^2=14*x^6+6*x^5+22*x^4+19*x^3+10*x^2+2*x+12", "y^2=30*x^5+14*x^4+7*x^3+5*x^2+3*x+3", "y^2=30*x^6+14*x^5+20*x^4+24*x^3+9*x^2+26*x+7", "y^2=x^6+15*x^5+8*x^4+6*x^3+2*x^2+30*x+12", "y^2=6*x^6+27*x^5+27*x^4+11*x^3+21*x^2+2*x+2", "y^2=26*x^6+14*x^5+18*x^4+9*x^3+11*x^2+x", "y^2=29*x^6+19*x^5+24*x^4+20*x^3+7*x^2+7*x+26", "y^2=17*x^6+29*x^5+15*x^4+16*x^3+26*x^2+6*x+6", "y^2=3*x^6+27*x^5+17*x^4+20*x^3+3*x^2+22*x+28", "y^2=23*x^6+11*x^5+x^4+11*x^3+x^2+12*x+26"], "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": 2, "g": 2, "galois_groups": ["4T3"], "geom_dim1_distinct": 0, "geom_dim1_factors": 0, "geom_dim2_distinct": 1, "geom_dim2_factors": 1, "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": 4, "geometric_extension_degree": 1, "geometric_galois_groups": ["4T3"], "geometric_number_fields": ["4.0.690421.1"], "geometric_splitting_field": "4.0.690421.1", "geometric_splitting_polynomials": [[659, -43, 48, -1, 1]], "group_structure_count": 2, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 26, "is_cyclic": false, "is_geometrically_simple": true, "is_geometrically_squarefree": true, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 26, "label": "2.31.aj_da", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 2, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [2], "number_fields": ["4.0.690421.1"], "p": 31, "p_rank": 2, "p_rank_deficit": 0, "pic_prime_gens": [[1, 3, 1, 13]], "poly": [1, -9, 78, -279, 961], "poly_str": "1 -9 78 -279 961 ", "primitive_models": [], "principal_polarization_count": 26, "q": 31, "real_poly": [1, -9, 16], "simple_distinct": ["2.31.aj_da"], "simple_factors": ["2.31.aj_daA"], "simple_multiplicities": [1], "singular_primes": ["2,-F-5"], "size": 26, "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.690421.1", "splitting_polynomials": [[659, -43, 48, -1, 1]], "twist_count": 2, "twists": [["2.31.j_da", "2.961.cx_eku", 2]], "weak_equivalence_count": 2, "zfv_index": 2, "zfv_index_factorization": [[2, 1]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_pic_size": 13, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 9556, "zfv_singular_count": 2, "zfv_singular_primes": ["2,-F-5"]}