# Stored data for abelian variety isogeny class 2.13.ag_x, downloaded from the LMFDB on 15 July 2026.
{"abvar_count": 109, "abvar_counts": [109, 30193, 4752400, 808961049, 138302871229, 23337401574400, 3937934738438341, 665416218448392489, 112457799488204352400, 19005057939452356391953], "abvar_counts_str": "109 30193 4752400 808961049 138302871229 23337401574400 3937934738438341 665416218448392489 112457799488204352400 19005057939452356391953 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 1, "angle_rank": 1, "angles": [0.146166291522335, 0.520500375144332], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 8, "curve_counts": [8, 180, 2162, 28324, 372488, 4834950, 62757416, 815730244, 10604724986, 137859174900], "curve_counts_str": "8 180 2162 28324 372488 4834950 62757416 815730244 10604724986 137859174900 ", "curves": ["y^2=x^6+12*x^5+9*x^4+4*x^2+8*x+11", "y^2=5*x^6+12*x^5+9*x^4+8*x^3+8*x^2+5*x+7", "y^2=9*x^6+x^5+3*x^4+9*x^3+x^2+4*x+6", "y^2=3*x^6+11*x^4+9*x^3+5*x^2+7*x+12", "y^2=4*x^6+x^5+2*x^4+3*x^3+10*x^2+8", "y^2=7*x^6+4*x^5+9*x^4+8*x^3+12*x^2+9*x+1", "y^2=7*x^6+x^5+12*x^3+6*x^2+7*x+12", "y^2=6*x^6+x^5+7*x^4+7*x^2+3*x+4", "y^2=5*x^6+11*x^5+3*x^4+4*x^3+2*x^2+x+11", "y^2=6*x^6+11*x^5+12*x^4+x^3+10*x^2+x+5", "y^2=5*x^6+12*x^5+3*x^4+8*x^3+6*x^2+10*x+5", "y^2=5*x^6+3*x^5+11*x^4+12*x^3+6*x^2+5*x+12"], "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": 4, "g": 2, "galois_groups": ["4T2"], "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": 3, "geometric_galois_groups": ["2T1"], "geometric_number_fields": ["2.0.4.1"], "geometric_splitting_field": "2.0.4.1", "geometric_splitting_polynomials": [[1, 0, 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": false, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 12, "label": "2.13.ag_x", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 24, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [], "number_fields": ["4.0.144.1"], "p": 13, "p_rank": 2, "p_rank_deficit": 0, "pic_prime_gens": [[1, 13, 1, 4]], "poly": [1, -6, 23, -78, 169], "poly_str": "1 -6 23 -78 169 ", "primitive_models": [], "principal_polarization_count": 12, "q": 13, "real_poly": [1, -6, -3], "simple_distinct": ["2.13.ag_x"], "simple_factors": ["2.13.ag_xA"], "simple_multiplicities": [1], "singular_primes": ["2,-F+V-5", "23,-F^2-4*F+2*V+2"], "size": 8, "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.144.1", "splitting_polynomials": [[1, 0, -1, 0, 1]], "twist_count": 16, "twists": [["2.13.g_x", "2.169.k_acr", 2], ["2.13.m_ck", "2.2197.abk_gzm", 3], ["2.13.ae_d", "2.28561.aje_bpod", 4], ["2.13.e_d", "2.28561.aje_bpod", 4], ["2.13.am_ck", "2.4826809.mbc_cfjsuo", 6], ["2.13.a_ak", "2.4826809.mbc_cfjsuo", 6], ["2.13.ak_by", "2.23298085122481.abeglpc_rjwnwmwwio", 12], ["2.13.ai_bq", "2.23298085122481.abeglpc_rjwnwmwwio", 12], ["2.13.ac_c", "2.23298085122481.abeglpc_rjwnwmwwio", 12], ["2.13.a_k", "2.23298085122481.abeglpc_rjwnwmwwio", 12], ["2.13.c_c", "2.23298085122481.abeglpc_rjwnwmwwio", 12], ["2.13.i_bq", "2.23298085122481.abeglpc_rjwnwmwwio", 12], ["2.13.k_by", "2.23298085122481.abeglpc_rjwnwmwwio", 12], ["2.13.a_ay", "2.542800770374370512771595361.alfgptgsrc_bkwrmykskfbghcwwjtko", 24], ["2.13.a_y", "2.542800770374370512771595361.alfgptgsrc_bkwrmykskfbghcwwjtko", 24]], "weak_equivalence_count": 4, "zfv_index": 92, "zfv_index_factorization": [[2, 2], [23, 1]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_pic_size": 4, "zfv_plus_index": 2, "zfv_plus_index_factorization": [[2, 1]], "zfv_plus_norm": 529, "zfv_singular_count": 4, "zfv_singular_primes": ["2,-F+V-5", "23,-F^2-4*F+2*V+2"]}