# Stored data for abelian variety isogeny class 2.31.an_do, downloaded from the LMFDB on 08 January 2026.
{"abvar_count": 638, "abvar_counts": [638, 937860, 892967768, 852514740000, 819527410949258, 787707835035992640, 756961660848862323338, 727425406501557881040000, 699053603979873974826728888, 671790493190149177333127446500], "abvar_counts_str": "638 937860 892967768 852514740000 819527410949258 787707835035992640 756961660848862323338 727425406501557881040000 699053603979873974826728888 671790493190149177333127446500 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 0, "angle_rank": 2, "angles": [0.145000771012702, 0.413172001920289], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 19, "curve_counts": [19, 977, 29974, 923113, 28625629, 887554442, 27513258379, 852893716273, 26439621554794, 819628243511177], "curve_counts_str": "19 977 29974 923113 28625629 887554442 27513258379 852893716273 26439621554794 819628243511177 ", "curves": ["y^2=24*x^6+x^5+22*x^4+9*x^3+4*x^2+27*x+14", "y^2=3*x^6+12*x^5+10*x^4+2*x^3+21*x^2+17", "y^2=12*x^6+21*x^5+19*x^4+19*x^3+7*x^2+23*x+22", "y^2=23*x^6+15*x^5+4*x^4+x^3+21*x^2+20*x+22", "y^2=21*x^6+6*x^5+13*x^4+5*x^3+7*x^2+30*x+12", "y^2=19*x^6+26*x^5+15*x^4+21*x^3+7*x^2+2*x+14", "y^2=26*x^6+23*x^5+4*x^4+27*x^3+11*x^2+12*x+24", "y^2=11*x^6+21*x^5+16*x^3+21*x^2+3*x+29", "y^2=22*x^6+29*x^5+16*x^4+13*x^3+14*x^2+2", "y^2=22*x^6+4*x^5+25*x^4+25*x^3+25*x^2+26*x+21", "y^2=27*x^6+3*x^5+21*x^4+28*x^3+x^2+22*x+25", "y^2=16*x^6+4*x^5+10*x^4+30*x^3+13*x+9"], "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": 4, "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": 4, "geometric_extension_degree": 1, "geometric_galois_groups": ["2T1", "2T1"], "geometric_number_fields": ["2.0.24.1", "2.0.115.1"], "geometric_splitting_field": "4.0.7617600.2", "geometric_splitting_polynomials": [[535, -70, 71, -2, 1]], "group_structure_count": 1, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 12, "is_cyclic": true, "is_geometrically_simple": false, "is_geometrically_squarefree": true, "is_primitive": true, "is_simple": false, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 12, "label": "2.31.an_do", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 2, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [], "number_fields": ["2.0.24.1", "2.0.115.1"], "p": 31, "p_rank": 2, "p_rank_deficit": 0, "pic_prime_gens": [[1, 2, 1, 6], [1, 3, 1, 6], [1, 5, 1, 6], [2, 5, 1, 6]], "poly": [1, -13, 92, -403, 961], "poly_str": "1 -13 92 -403 961 ", "primitive_models": [], "principal_polarization_count": 16, "q": 31, "real_poly": [1, -13, 30], "simple_distinct": ["1.31.ak", "1.31.ad"], "simple_factors": ["1.31.akA", "1.31.adA"], "simple_multiplicities": [1, 1], "singular_primes": ["7,7*F+V+10", "7,2*F+5*V-52"], "size": 100, "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.7617600.2", "splitting_polynomials": [[535, -70, 71, -2, 1]], "twist_count": 4, "twists": [["2.31.ah_bg", "2.961.p_ado", 2], ["2.31.h_bg", "2.961.p_ado", 2], ["2.31.n_do", "2.961.p_ado", 2]], "weak_equivalence_count": 4, "zfv_index": 49, "zfv_index_factorization": [[7, 2]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_pic_size": 72, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 2760, "zfv_singular_count": 4, "zfv_singular_primes": ["7,7*F+V+10", "7,2*F+5*V-52"]}